  Mary Pyo

Measures of Central Tendency

Slide Duration:

Section 1: Algebra and Decimals
Expressions and Variables

5m 57s

Intro
0:00
Vocabulary
0:06
Variable
0:09
Expression
0:48
Numerical Expression
1:08
Algebraic Expression
1:35
Word Expression
2:04
Extra Example 1: Evaluate the Expression
2:27
Extra Example 2: Evaluate the Expression
3:16
Extra Example 3: Evaluate the Expression
4:04
Extra Example 4: Evaluate the Expression
4:59
Exponents

5m 34s

Intro
0:00
What Exponents Mean
0:07
Example: Ten Squared
0:08
Extra Example 1: Exponents
0:50
Extra Example 2: Write in Exponent Form
1:58
Extra Example 3: Using Exponent and Base
2:37
Extra Example 4: Write the Equal Factors
4:26
Order of Operations

8m 40s

Intro
0:00
Please Excuse My Dear Aunt Sally
0:07
Step 1: Parenthesis
1:16
Step 2: Exponent
1:25
Step 3: Multiply and Divide
1:30
2:00
Example: Please Excuse My Dear Aunt Sally
2:26
Extra Example 1: Evaluating Expression
3:37
Extra Example 2: Evaluating Expression
4:59
Extra Example 3: Evaluating Expression
5:34
Extra Example 4: Evaluating Expression
6:25
Comparing and Ordering Decimals

13m 37s

Intro
0:00
Place Value
0:13
Examples: 1,234,567.89
0:19
Which is the Larger Value?
1:33
Which is Larger: 10.5 or 100.5
1:46
Which is Larger: 1.01 or 1.10
2:24
Which is Larger: 44.40 or 44.4
4:20
Which is Larger: 18.6 or 16.8
5:18
Extra Example 1: Order from Least to Greatest
5:55
Extra Example 2: Order from Least to Greatest
7:56
Extra Example 3: Order from Least to Greatest
9:16
Extra Example 4: Order from Least to Greatest
10:42
Rounding Decimals

12m 31s

Intro
0:00
Decimal Place Value
0:06
Example: 12,3454.6789
0:07
How to Round Decimals
1:17
Example: Rounding 1,234.567
1:18
Extra Example 1: Rounding Decimals
3:47
Extra Example 2: Rounding Decimals
6:10
Extra Example 3: Rounding Decimals
7:45
Extra Example 4: Rounding Decimals
9:56

11m 30s

Intro
0:00
0:06
Align the Decimal Point First
0:12
0:47
Place the Decimal Point in the Same Place
0:55
Check by Estimating
1:09
Examples
1:28
Add: 3.45 + 7 + 0.835
1:30
Find the Difference: 351.4 - 65.25
3:34
5:32
Extra Example 2: How Much Money?
6:09
Extra Example 3: Subtracting Decimals
7:20
9:32
Multiplying Decimals

10m 30s

Intro
0:00
Multiply the Decimals
0:05
Methods for Multiplying Decimals
0:06
Example: 1.1 x 6
0:38
Extra Example 1: Multiplying Decimals
1:51
Extra Example 2: Work Money
2:49
Extra Example 3: Multiplying Decimals
5:45
Extra Example 4: Multiplying Decimals
7:46
Dividing Decimals

17m 49s

Intro
0:00
When Dividing Decimals
0:06
Methods for Dividing Decimals
0:07
Divisor and Dividend
0:37
Example: 0.2 Divided by 10
1:35
Extra Example 1 : Dividing Decimals
5:24
Extra Example 2: How Much Does Each CD Cost?
8:22
Extra Example 3: Dividing Decimals
10:59
Extra Example 4: Dividing Decimals
12:08
Section 2: Number Relationships and Fractions
Prime Factorization

7m

Intro
0:00
Terms to Review
0:07
Prime vs. Composite
0:12
Factor
0:54
Product
1:15
Factor Tree
1:39
Example: Prime Factorization
2:01
Example: Prime Factorization
2:43
Extra Example 1: Prime Factorization
4:08
Extra Example 2: Prime Factorization
5:05
Extra Example 3: Prime Factorization
5:33
Extra Example 4: Prime Factorization
6:13
Greatest Common Factor

12m 47s

Intro
0:00
Terms to Review
0:05
Factor
0:07
Example: Factor of 20
0:18
Two Methods
0:59
Greatest Common Factor
1:00
Method 1: GCF of 15 and 30
1:37
Method 2: GCF of 15 and 30
2:58
Extra Example 1: Find the GCF of 6 and 18
5:16
Extra Example 2: Find the GCF of 36 and 27
7:43
Extra Example 3: Find the GCF of 6 and 18
9:18
Extra Example 4: Find the GCF of 54 and 36
10:30
Fraction Concepts and Simplest Form

10m 3s

Intro
0:00
Fraction Concept
0:10
Example: Birthday Cake
0:28
Example: Chocolate Bar
2:10
Simples Form
3:38
Example: Simplifying 4 out of 8
3:46
Extra Example 1: Graphically Show 4 out of 10
4:41
Extra Example 2: Finding Fraction Shown by Illustration
5:10
Extra Example 3: Simplest Form of 5 over 25
7:02
Extra Example 4: Simplest Form of 14 over 49
8:30
Least Common Multiple

14m 16s

Intro
0:00
Term to Review
0:06
Multiple
0:07
Example: Multiples of 4
0:15
Two Methods
0:41
Least Common Multiples
0:44
Method 1: LCM of 6 and 10
1:09
Method 2: LCM of 6 and 10
2:56
Extra Example 1: LCM of 12 and 15
5:09
Extra Example 2: LCM of 16 and 20
7:36
Extra Example 3 : LCM of 15 and 25
10:00
Extra Example 4 : LCM of 12 and 18
11:27
Comparing and Ordering Fractions

13m 10s

Intro
0:00
Terms Review
0:14
Greater Than
0:16
Less Than
0:40
Compare the Fractions
1:00
Example: Comparing 2/4 and 3/4
1:08
Example: Comparing 5/8 and 2/5
2:04
Extra Example 1: Compare the Fractions
3:28
Extra Example 2: Compare the Fractions
6:06
Extra Example 3: Compare the Fractions
8:01
Extra Example 4: Least to Greatest
9:37
Mixed Numbers and Improper Fractions

12m 49s

Intro
0:00
Fractions
0:10
Mixed Number
0:21
Proper Fraction
0:47
Improper Fraction
1:30
Switching Between
2:47
Mixed Number to Improper Fraction
2:53
Improper Fraction to Mixed Number
4:41
Examples: Switching Fractions
6:37
Extra Example 1: Mixed Number to Improper Fraction
8:57
Extra Example 2: Improper Fraction to Mixed Number
9:37
Extra Example 3: Improper Fraction to Mixed Number
10:21
Extra Example 4: Mixed Number to Improper Fraction
11:31
Connecting Decimals and Fractions

15m 1s

Intro
0:00
Examples: Decimals and Fractions
0:06
More Examples: Decimals and Fractions
2:48
Extra Example 1: Converting Decimal to Fraction
6:55
Extra Example 2: Converting Fraction to Decimal
8:45
Extra Example 3: Converting Decimal to Fraction
10:28
Extra Example 4: Converting Fraction to Decimal
11:42
Section 3: Fractions and Their Operations
Adding and Subtracting Fractions with Same Denominators

5m 17s

Intro
0:00
Same Denominator
0:11
Numerator and Denominator
0:18
Example: 2/6 + 5/6
0:41
Extra Example 1: Add or Subtract the Fractions
2:02
Extra Example 2: Add or Subtract the Fractions
2:45
Extra Example 3: Add or Subtract the Fractions
3:17
Extra Example 4: Add or Subtract the Fractions
4:05
Adding and Subtracting Fractions with Different Denominators

23m 8s

Intro
0:00
Least Common Multiple
0:12
LCM of 6 and 4
0:31
From LCM to LCD
2:25
3:12
Extra Example 1: Add or Subtract
6:23
Extra Example 2: Add or Subtract
9:49
Extra Example 3: Add or Subtract
14:54
Extra Example 4: Add or Subtract
18:14

19m 44s

Intro
0:00
Example
0:05
0:17
Extra Example 1: Adding Mixed Numbers
1:57
Extra Example 2: Subtracting Mixed Numbers
8:13
Extra Example 3: Adding Mixed Numbers
12:01
Extra Example 4: Subtracting Mixed Numbers
14:54
Multiplying Fractions and Mixed Numbers

21m 32s

Intro
0:00
Multiplying Fractions
0:07
Step 1: Change Mixed Numbers to Improper Fractions
0:08
Step2: Multiply the Numerators Together
0:56
Step3: Multiply the Denominators Together
1:03
Extra Example 1: Multiplying Fractions
1:37
Extra Example 2: Multiplying Fractions
6:39
Extra Example 3: Multiplying Fractions
10:20
Extra Example 4: Multiplying Fractions
13:47
Dividing Fractions and Mixed Numbers

18m

Intro
0:00
Dividing Fractions
0:09
Step 1: Change Mixed Numbers to Improper Fractions
0:15
Step 2: Flip the Second Fraction
0:27
Step 3: Multiply the Fractions
0:52
Extra Example 1: Dividing Fractions
1:23
Extra Example 2: Dividing Fractions
5:06
Extra Example 3: Dividing Fractions
9:34
Extra Example 4: Dividing Fractions
12:06
Distributive Property

11m 5s

Intro
0:00
Distributive Property
0:06
Methods of Distributive Property
0:07
Example: a(b)
0:35
Example: a(b+c)
0:49
Example: a(b+c+d)
1:22
Extra Example 1: Using Distributive Property
1:56
Extra Example 2: Using Distributive Property
4:36
Extra Example 3: Using Distributive Property
6:39
Extra Example 4: Using Distributive Property
8:19
Units of Measure

16m 36s

Intro
0:00
Length
0:05
Feet, Inches, Yard, and Mile
0:20
Millimeters, Centimeters, and Meters
0:43
Mass
2:57
Pounds, Ounces, and Tons
3:03
Grams and Kilograms
3:38
Liquid
4:11
Gallons, Quarts, Pints, and Cups
4:14
Extra Example 1: Converting Units
7:02
Extra Example 2: Converting Units
9:31
Extra Example 3: Converting Units
12:21
Extra Example 4: Converting Units
14:05
Section 4: Positive and Negative Numbers
Integers and the Number Line

13m 24s

Intro
0:00
What are Integers
0:06
Integers are all Whole Numbers and Their Opposites
0:09
Absolute Value
2:35
Extra Example 1: Compare the Integers
4:36
Extra Example 2: Writing Integers
9:24
Extra Example 3: Opposite Integer
10:38
Extra Example 4: Absolute Value
11:27

16m 5s

Intro
0:00
Using a Number Line
0:04
Example: 4 + (-2)
0:14
Example: 5 + (-8)
1:50
3:00
3:10
3:37
4:44
Extra Example 1: Add the Integers
8:21
Extra Example 2: Find the Sum
10:33
Extra Example 3: Find the Value
11:37
Extra Example 4: Add the Integers
13:10
Subtracting Integers

15m 25s

Intro
0:00
How to Subtract Integers
0:06
Two-dash Rule
0:16
Example: 3 - 5
0:44
Example: 3 - (-5)
1:12
Example: -3 - 5
1:39
Extra Example 1: Rewrite Subtraction to Addition
4:43
Extra Example 2: Find the Difference
7:59
Extra Example 3: Find the Difference
9:08
Extra Example 4: Evaluate
10:38
Multiplying Integers

7m 33s

Intro
0:00
When Multiplying Integers
0:05
If One Number is Negative
0:06
If Both Numbers are Negative
0:18
Examples: Multiplying Integers
0:53
Extra Example 1: Multiplying Integers
1:27
Extra Example 2: Multiplying Integers
2:43
Extra Example 3: Multiplying Integers
3:13
Extra Example 4: Multiplying Integers
3:51
Dividing Integers

6m 42s

Intro
0:00
When Dividing Integers
0:05
Rules for Dividing Integers
0:41
Extra Example 1: Dividing Integers
1:01
Extra Example 2: Dividing Integers
1:51
Extra Example 3: Dividing Integers
2:21
Extra Example 4: Dividing Integers
3:18
Integers and Order of Operations

11m 9s

Intro
0:00
Combining Operations
0:21
Solve Using the Order of Operations
0:22
Extra Example 1: Evaluate
1:18
Extra Example 2: Evaluate
4:20
Extra Example 3: Evaluate
6:33
Extra Example 4: Evaluate
8:13
Section 5: Solving Equations
Writing Expressions

9m 15s

Intro
0:00
Operation as Words
0:05
Operation as Words
0:06
Extra Example 1: Write Each as an Expression
2:09
Extra Example 2: Write Each as an Expression
4:27
Extra Example 3: Write Each Expression Using Words
6:45
Writing Equations

18m 3s

Intro
0:00
Equation
0:05
Definition of Equation
0:06
Examples of Equation
0:58
Operations as Words
1:39
Operations as Words
1:40
Extra Example 1: Write Each as an Equation
3:07
Extra Example 2: Write Each as an Equation
6:19
Extra Example 3: Write Each as an Equation
10:08
Extra Example 4: Determine if the Equation is True or False
13:38

24m 53s

Intro
0:00
Solving Equations
0:08
inverse Operation of Addition and Subtraction
0:09
Extra Example 1: Solve Each Equation Using Mental Math
4:15
Extra Example 2: Use Inverse Operations to Solve Each Equation
5:44
Extra Example 3: Solve Each Equation
14:51
Extra Example 4: Translate Each to an Equation and Solve
19:57
Solving Multiplication Equation

19m 46s

Intro
0:00
Multiplication Equations
0:08
Inverse Operation of Multiplication
0:09
Extra Example 1: Use Mental Math to Solve Each Equation
3:54
Extra Example 2: Use Inverse Operations to Solve Each Equation
5:55
Extra Example 3: Is -2 a Solution of Each Equation?
12:48
Extra Example 4: Solve Each Equation
15:42
Solving Division Equation

17m 58s

Intro
0:00
Division Equations
0:05
Inverse Operation of Division
0:06
Extra Example 1: Use Mental Math to Solve Each Equation
0:39
Extra Example 2: Use Inverse Operations to Solve Each Equation
2:14
Extra Example 3: Is -6 a Solution of Each Equation?
9:53
Extra Example 4: Solve Each Equation
11:50
Section 6: Ratios and Proportions
Ratio

40m 21s

Intro
0:00
Ratio
0:05
Definition of Ratio
0:06
Examples of Ratio
0:18
Rate
2:19
Definition of Rate
2:20
Unit Rate
3:38
Example: \$10 / 20 pieces
5:05
Converting Rates
6:46
Example: Converting Rates
6:47
Extra Example 1: Write in Simplest Form
16:22
Extra Example 2: Find the Ratio
20:53
Extra Example 3: Find the Unit Rate
22:56
Extra Example 4: Convert the Unit
26:34
Solving Proportions

17m 22s

Intro
0:00
Proportions
0:05
An Equality of Two Ratios
0:06
Cross Products
1:00
Extra Example 1: Find Two Equivalent Ratios for Each
3:21
Extra Example 2: Use Mental Math to Solve the Proportion
5:52
Extra Example 3: Tell Whether the Two Ratios Form a Proportion
8:21
Extra Example 4: Solve the Proportion
13:26
Writing Proportions

22m 1s

Intro
0:00
Writing Proportions
0:08
Introduction to Writing Proportions and Example
0:10
Extra Example 1: Write a Proportion and Solve
5:54
Extra Example 2: Write a Proportion and Solve
11:19
Extra Example 3: Write a Proportion for Word Problem
17:29
Similar Polygons

16m 31s

Intro
0:00
Similar Polygons
0:05
Definition of Similar Polygons
0:06
Corresponding Sides are Proportional
2:14
Extra Example 1: Write a Proportion and Find the Value of Similar Triangles
4:26
Extra Example 2: Write a Proportional to Find the Value of x
7:04
Extra Example 3: Write a Proportion for the Similar Polygons and Solve
9:04
Extra Example 4: Word Problem and Similar Polygons
11:03
Scale Drawings

13m 43s

Intro
0:00
Scale Drawing
0:05
Definition of a Scale Drawing
0:06
Example: Scale Drawings
1:00
Extra Example 1: Scale Drawing
4:50
Extra Example 2: Scale Drawing
7:02
Extra Example 3: Scale Drawing
9:34
Probability

11m 51s

Intro
0:00
Probability
0:05
Introduction to Probability
0:06
Example: Probability
1:22
Extra Example 1: What is the Probability of Landing on Orange?
3:26
Extra Example 2: What is the Probability of Rolling a 5?
5:02
Extra Example 3: What is the Probability that the Marble will be Red?
7:40
Extra Example 4: What is the Probability that the Student will be a Girl?
9:43
Section 7: Percents
Percents, Fractions, and Decimals

35m 5s

Intro
0:00
Percents
0:06
Changing Percent to a Fraction
0:07
Changing Percent to a Decimal
1:54
Fractions
4:17
Changing Fraction to Decimal
4:18
Changing Fraction to Percent
7:50
Decimals
10:10
Changing Decimal to Fraction
10:11
Changing Decimal to Percent
12:07
Extra Example 1: Write Each Percent as a Fraction in Simplest Form
13:29
Extra Example 2: Write Each as a Decimal
17:09
Extra Example 3: Write Each Fraction as a Percent
22:45
Extra Example 4: Complete the Table
29:17
Finding a Percent of a Number

28m 18s

Intro
0:00
Percent of a Number
0:06
Translate Sentence into an Equation
0:07
Example: 30% of 100 is What Number?
1:05
Extra Example 1: Finding a Percent of a Number
7:12
Extra Example 2: Finding a Percent of a Number
15:56
Extra Example 3: Finding a Percent of a Number
19:14
Extra Example 4: Finding a Percent of a Number
24:26
Solving Percent Problems

32m 31s

Intro
0:00
Solving Percent Problems
0:06
Translate the Sentence into an Equation
0:07
Extra Example 1: Solving Percent Problems
0:56
Extra Example 2: Solving Percent Problems
14:49
Extra Example 3: Solving Percent Problems
23:44
Simple Interest

27m 9s

Intro
0:00
Simple Interest
0:05
Principal
0:06
Interest & Interest Rate
0:41
Simple Interest
1:43
Simple Interest Formula
2:23
Simple Interest Formula: I = prt
2:24
Extra Example 1: Finding Simple Interest
3:53
Extra Example 2: Finding Simple Interest
8:08
Extra Example 3: Finding Simple Interest
12:02
Extra Example 4: Finding Simple Interest
17:46
Discount and Sales Tax

17m 15s

Intro
0:00
Discount
0:19
Discount
0:20
Sale Price
1:22
Sales Tax
2:24
Sales Tax
2:25
Total Due
2:59
Extra Example 1: Finding the Discount
3:43
Extra Example 2: Finding the Sale Price
6:28
Extra Example 3: Finding the Sale Tax
11:14
Extra Example 4: Finding the Total Due
14:08
Section 8: Geometry in a Plane
Intersecting Lines and Angle Measures

24m 17s

Intro
0:00
Intersecting Lines
0:07
Properties of Lines
0:08
When Two Lines Cross Each Other
1:55
Angles
2:56
Properties of Angles: Sides, Vertex, and Measure
2:57
Classifying Angles
7:18
Acute Angle
7:19
Right Angle
7:54
Obtuse Angle
8:03
Angle Relationships
8:56
Vertical Angles
8:57
10:38
Complementary Angles
11:52
Supplementary Angles
12:54
Extra Example 1: Lines
16:00
Extra Example 2: Angles
18:22
Extra Example 3: Angle Relationships
20:05
Extra Example 4: Name the Measure of Angles
21:11
Angles of a Triangle

13m 35s

Intro
0:00
Angles of a Triangle
0:05
All Triangles Have Three Angles
0:06
Measure of Angles
2:16
Extra Example 1: Find the Missing Angle Measure
5:39
Extra Example 2: Angles of a Triangle
7:18
Extra Example 3: Angles of a Triangle
9:24
Classifying Triangles

15m 10s

Intro
0:00
Types of Triangles by Angles
0:05
Acute Triangle
0:06
Right Triangle
1:14
Obtuse Triangle
2:22
Classifying Triangles by Sides
4:18
Equilateral Triangle
4:20
Isosceles Triangle
5:21
Scalene Triangle
5:53
Extra Example 1: Classify the Triangle by Its Angles and Sides
6:34
Extra Example 2: Sketch the Figures
8:10
Extra Example 3: Classify the Triangle by Its Angles and Sides
9:55
Extra Example 4: Classify the Triangle by Its Angles and Sides
11:35

17m 41s

Intro
0:00
0:05
0:06
Parallelogram
0:45
Rectangle
2:28
Rhombus
3:13
Square
3:53
Trapezoid
4:38
Parallelograms
5:33
Parallelogram, Rectangle, Rhombus, Trapezoid, and Square
5:35
Extra Example 1: Give the Most Exact Name for the Figure
11:37
Extra Example 2: Fill in the Blanks
13:31
Extra Example 3: Complete Each Statement with Always, Sometimes, or Never
14:37
Area of a Parallelogram

12m 44s

Intro
0:00
Area
0:06
Definition of Area
0:07
Area of a Parallelogram
2:00
Area of a Parallelogram
2:01
Extra Example 1: Find the Area of the Rectangle
4:30
Extra Example 2: Find the Area of the Parallelogram
5:29
Extra Example 3: Find the Area of the Parallelogram
7:22
Extra Example 4: Find the Area of the Shaded Region
8:55
Area of a Triangle

11m 29s

Intro
0:00
Area of a Triangle
0:05
Area of a Triangle: Equation and Example
0:06
Extra Example 1: Find the Area of the Triangles
1:31
Extra Example 2: Find the Area of the Figure
4:09
Extra Example 3: Find the Area of the Shaded Region
7:45
Circumference of a Circle

15m 4s

Intro
0:00
Segments in Circles
0:05
0:06
Diameter
1:08
Chord
1:49
Circumference
2:53
Circumference of a Circle
2:54
Extra Example 1: Name the Given Parts of the Circle
6:26
Extra Example 2: Find the Circumference of the Circle
7:54
Extra Example 3: Find the Circumference of Each Circle with the Given Measure
11:04
Area of a Circle

14m 43s

Intro
0:00
Area of a Circle
0:05
Area of a Circle: Equation and Example
0:06
Extra Example 1: Find the Area of the Circle
2:17
Extra Example 2: Find the Area of the Circle
5:47
Extra Example 3: Find the Area of the Shaded Region
9:24
Section 11: Geometry in Space
Prisms and Cylinders

21m 49s

Intro
0:00
Prisms
0:06
Polyhedron
0:07
Regular Prism, Bases, and Lateral Faces
1:44
Cylinders
9:37
Bases and Altitude
9:38
Extra Example 1: Classify Each Prism by the Shape of Its Bases
11:16
Extra Example 2: Name Two Different Edges, Faces, and Vertices of the Prism
15:44
Extra Example 3: Name the Solid of Each Object
17:58
Extra Example 4: Write True or False for Each Statement
19:47
Volume of a Rectangular Prism

8m 59s

Intro
0:00
Volume of a Rectangular Prism
0:06
Volume of a Rectangular Prism: Formula
0:07
Volume of a Rectangular Prism: Example
1:46
Extra Example 1: Find the Volume of the Rectangular Prism
3:39
Extra Example 2: Find the Volume of the Cube
5:00
Extra Example 3: Find the Volume of the Solid
5:56
Volume of a Triangular Prism

16m 15s

Intro
0:00
Volume of a Triangular Prism
0:06
Volume of a Triangular Prism: Formula
0:07
Extra Example 1: Find the Volume of the Triangular Prism
2:42
Extra Example 2: Find the Volume of the Triangular Prism
7:21
Extra Example 3: Find the Volume of the Solid
10:38
Volume of a Cylinder

15m 55s

Intro
0:00
Volume of a Cylinder
0:05
Volume of a Cylinder: Formula
0:06
Extra Example 1: Find the Volume of the Cylinder
1:52
Extra Example 2: Find the Volume of the Cylinder
7:38
Extra Example 3: Find the Volume of the Cylinder
11:25
Surface Area of a Prism

23m 28s

Intro
0:00
Surface Area of a Prism
0:06
Surface Area of a Prism
0:07
Lateral Area of a Prism
2:12
Lateral Area of a Prism
2:13
Extra Example 1: Find the Surface Area of the Rectangular Prism
7:08
Extra Example 2: Find the Lateral Area and the Surface Area of the Cube
12:05
Extra Example 3: Find the Surface Area of the Triangular Prism
17:13
Surface Area of a Cylinder

27m 41s

Intro
0:00
Surface Area of a Cylinder
0:06
Introduction to Surface Area of a Cylinder
0:07
Surface Area of a Cylinder
1:33
Formula
1:34
Extra Example 1: Find the Surface Area of the Cylinder
5:51
Extra Example 2: Find the Surface Area of the Cylinder
13:51
Extra Example 3: Find the Surface Area of the Cylinder
20:57
Section 10: Data Analysis and Statistics
Measures of Central Tendency

24m 32s

Intro
0:00
Measures of Central Tendency
0:06
Mean
1:17
Median
2:42
Mode
5:41
Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data
6:24
Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data
11:14
Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data
15:13
Extra Example 4: Find the Three Measures of the Central Tendency
19:12
Histograms

19m 43s

Intro
0:00
Histograms
0:05
Definition and Example
0:06
Extra Example 1: Draw a Histogram for the Frequency Table
6:14
Extra Example 2: Create a Histogram of the Data
8:48
Extra Example 3: Create a Histogram of the Following Test Scores
14:17
Box-and-Whisker Plot

17m 54s

Intro
0:00
Box-and-Whisker Plot
0:05
Median, Lower & Upper Quartile, Lower & Upper Extreme
0:06
Extra Example 1: Name the Median, Lower & Upper Quartile, Lower & Upper Extreme
6:04
Extra Example 2: Draw a Box-and-Whisker Plot Given the Information
7:35
Extra Example 3: Find the Median, Lower & Upper Quartile, Lower & Upper Extreme
9:31
Extra Example 4: Draw a Box-and-Whiskers Plots for the Set of Data
12:50
Stem-and-Leaf Plots

17m 42s

Intro
0:00
Stem-and-Leaf Plots
0:05
Stem-and-Leaf Plots
0:06
Extra Example 1: Use the Data to Create a Stem-and-Leaf Plot
2:28
Extra Example 2: List All the Numbers in the Stem-and-Leaf Plot in Order From Least to Greatest
7:02
Extra Example 3: Create a Stem-and-Leaf Plot of the Data & Find the Median and the Mode.
8:59
The Coordinate Plane

19m 59s

Intro
0:00
The Coordinate System
0:05
The Coordinate Plane
0:06
0:50
The Coordinate Plane
7:02
Write the Coordinates for Points A, B, and C
7:03
Extra Example 1: Graph Each Point on the Coordinate Plane
9:03
Extra Example 2: Write the Coordinate and Quadrant for Each Point
11:05
Extra Example 3: Name Two Points From Each of the Four Quadrants
13:13
Extra Example 4: Graph Each Point on the Same Coordinate Plane
17:47
Section 11: Probability and Discrete Mathematics
Organizing Possible Outcomes

15m 35s

Intro
0:00
Compound Events
0:08
Compound Events
0:09
Fundamental Counting Principle
3:35
Extra Example 1: Create a List of All the Possible Outcomes
4:47
Extra Example 2: Create a Tree Diagram For All the Possible Outcomes
6:34
Extra Example 3: Create a Tree Diagram For All the Possible Outcomes
10:00
Extra Example 4: Fundamental Counting Principle
12:41
Independent and Dependent Events

35m 19s

Intro
0:00
Independent Events
0:11
Definition
0:12
Example 1: Independent Event
1:45
Example 2: Two Independent Events
4:48
Dependent Events
9:09
Definition
9:10
Example: Dependent Events
10:10
Extra Example 1: Determine If the Two Events are Independent or Dependent Events
13:38
Extra Example 2: Find the Probability of Each Pair of Events
18:11
Extra Example 3: Use the Spinner to Find Each Probability
21:42
Extra Example 4: Find the Probability of Each Pair of Events
25:49
Disjoint Events

12m 13s

Intro
0:00
Disjoint Events
0:06
Definition and Example
0:07
Extra Example 1: Disjoint & Not Disjoint Events
3:08
Extra Example 2: Disjoint & Not Disjoint Events
4:23
Extra Example 3: Independent, Dependent, and Disjoint Events
6:30
Probability of an Event Not Occurring

20m 5s

Intro
0:00
Event Not Occurring
0:07
Formula and Example
0:08
Extra Example 1: Use the Spinner to Find Each Probability
7:24
Extra Example 2: Probability of Event Not Occurring
11:21
Extra Example 3: Probability of Event Not Occurring
15:51
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• ## Related Books 0 answersPost by Milan Ray on April 15, 2014This is hard even I already know this 4 answersLast reply by: Mingyang CenWed Aug 15, 2018 8:18 PMPost by Samvel Karapetyan on May 11, 2012What if the mode is 1,2,2,3,3,4....?

### Measures of Central Tendency

• The three measures of central tendency help describe a set of data
• Mean is the sum of the numbers divided by the number of addends (average)
• Median is the middle number when arranged in numerical order (middle)
• Mode is the number that occurs most often (most)

### Measures of Central Tendency

Find the mean, median and mode for the following set of data.
(15,25,5,10,20)
• Mean: [(15 + 25 + 5 + 10 + 20)/5] = [75/5] = 15
• Median: 5,10,15,20,25
• Mode: None
Mean:15, Median:15, Mode: None
Find the mean, median and mode for the following set of data.
(15,25,5,11)
• Mean: [(15 + 25 + 5 + 11)/4] = [56/4] = 14
• Median: 5,11,15,25 = [(11 + 15)/2] = 13
• Mode: None
Mean:14, Median:13, Mode: None
Find the mean, median and mode for the following set of data.
(5,25,5,13)
• Mean: [(5 + 25 + 5 + 13)/4] = [48/4] = 12
• Median: 5,5,13,25 = [(5 + 13)/2] = 9
• Mode: 5
Mean:12, Median:9, Mode: 5
Find the mean, median and mode for the following set of data.
(3,2,3,3,4)
• Mean: [(3 + 2 + 3 + 3 + 4)/5] = [15/5] = 3
• Median: 2,3,3,3,4
• Mode: 3
Mean:3, Median:3, Mode: 3
Find the mean, median and mode for the following set of data.
(4,4,4,2,6)
• Mean: [(4 + 4 + 4 + 2 + 6)/5] = [20/5] = 4
• Median: 2,4,4,4,6
• Mode: 4
Mean:4, Median:4, Mode: 4
Sarah's test score for the last five chapters are 50, 100, 85, 95, and 90. Find the mode, mean, and median of her scores.
• Mean: [(50 + 100 + 85 + 95 + 90)/5] = [420/5] = 84
• Median: 50,85,90,95,100
• Mode: None
Mean:84, Median:90, Mode: None
Sarah's test score for the last five chapters are 100, 100, 85, 95, and 90. Find the mode, mean, and median of her scores.
• Mean: [(100 + 100 + 85 + 95 + 90)/5] = [470/5] = 94
• Median: 85,90,95,100,100
• Mode: 100
Mean:94, Median:95, Mode: 100
Sarah's test score for the last four chapters are 100, 85, 95, and 92. Find the mode, mean, and median of her scores.
• Mean: [(100 + 85 + 95 + 92)/4] = [372/4] = 93
• Median: 85,92,95,100 = [(92 + 95)/2] = 93.5
• Mode: None
Mean:93, Median:93.5, Mode: None
The daily temperatures for the last few days were 45, 16, 32, 16, 12, and 17. Find the three measures of central tendency.
• Mean: [(45 + 16 + 32 + 16 + 12 + 17)/6] = [138/6] = 29
• Median: 12,16,16 ,17 ,32,45 = [(16 + 17)/2] = 16.5
• Mode: 16
Mean:29, Median:16.5, Mode: 16
The daily temperatures for the last few days were 72,96,72,75, and 80. Find the three measures of central tendency.
• Mean: [(72 + 96 + 72 + 75 + 80)/5] = [395/5] = 79
• Median: 72,72,75 ,80,96 = 75
• Mode: 72
Mean:79, Median:75, Mode: 72

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Measures of Central Tendency

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Measures of Central Tendency 0:06
• Mean
• Median
• Mode
• Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data 6:24
• Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data 11:14
• Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data 15:13
• Extra Example 4: Find the Three Measures of the Central Tendency 19:12

### Transcription: Measures of Central Tendency

Welcome back to Educator.com.0000

For the next lesson, we are going to go over measures of central tendency.0002

The measures of central tendency are just three different types of ways you can describe data.0008

If you have a set of numbers, if you have some numbers,0018

then there are three ways you can represent the measures of those numbers.0022

The first one, the first measure of central tendency is the mean.0031

The mean is the sum of all the numbers divided by however many numbers you have.0035

Another word for it is average.0043

You are looking for the average of all the numbers in your data.0044

The next one is median.0049

Median is when you list out all the numbers in order from least to greatest,0051

you are going to find the middle number, the one that is right in the middle.0058

That is called the median; the key word here is middle.0062

The third one is the mode; the mode is the number that occurs the most.0067

It is the number that you see the most in your set of data.0072

The keyword here is going to be most.0075

Let's say if I have a set of numbers, let's say 1, 2, 3, 4, and 5.0080

The mean, keyword average, we are going to find the average of all those numbers.0087

We are going to add them all up; 1 plus 2 plus 3 plus 4 plus 5.0095

You are going to divide by however many numbers you have.0102

Here we have five different numbers; you are going to divide that sum by 5.0107

1 plus 2 is 3.0115

I am just going to write that number on top like that.0118

That is 3 plus 3 is 6; 6 plus 4 is 10; 10 plus 5 is 15.0122

This looks like a fraction... if I write it like... I am sorry; wrote the wrong number.0130

5... if write it like that, it looks like a fraction.0138

But fractions are division; you can just think of that as 15 divided by 5.0141

15 divided by 5; we know that 5 goes into 15 three times.0148

15 divided by 5 is 3; the mean is 3.0154

That is the average of those five numbers.0160

The median of that set of data is going to the middle number0164

but only when you list it out in order from least to greatest.0170

You must list it out.0174

Here it is already listed from least to greatest; 1, 2, 3, 4, 5.0177

The number in the middle will be this number right there; the median is 3.0184

When you have two numbers in the middle, let's say you have an even number of numbers.0196

Say it is just 1, 2, 3, and 4.0202

If that is your data, you have two numbers in the middle.0207

Then you are going to find the average between those two numbers.0212

We are going to add those two numbers and divide it by 2.0216

That will be 2 plus 3 divided by... there is only two numbers there so it is 2.0220

That is going to be 5/2.0227

You can usually leave it as a fraction.0231

If you want, you can change it to a mixed number.0234

How many times does 2 fit into 5?--2 fits into 5 two times.0236

You have 1 left over; keep your same denominator.0243

That is how you change... this is called an improper fraction0248

when the number on the top is bigger than the number on the bottom.0251

You can change it to a mixed number where you are going to have a whole number and then a proper fraction.0255

Again 2 fits into 5 two times; that becomes your whole number, 2.0263

You can leave it like that.0271

Or if you want, you can just do 5 divided by 2, and change it to a decimal.0273

Remember 5, this top number, goes inside; that is on the outside.0283

Put a decimal point at the end of that number; bring it up.0290

2 fits into 5 twice; that is a 4; we subtract; get 1.0293

I can add 0s there at the end of that number behind the decimal point.0301

Bring that 0 down; 2 goes into 10 five times.0307

That is 10; my remainder is 0.0314

Your median here, when we find the average of that, will either be 2 and 1/2 or 2.5.0318

You could just think of it as halfway between 2 and 3.0330

That is the average; between 2 and 3 is going to be 2 and 1/2; 2.5.0334

The third one, the mode, remember the keyword here is most.0342

It is the one that you see the most.0346

Here with our set of data, 1, 2, 3, 4, 5, you only see each of the numbers one time.0350

In this case, we have no mode.0359

If you had 1, 2, 2, and 3, then you know the mode would be 2 because you see that number the most.0363

It occurs the most; that is the mode.0373

Again mean is average; median is middle; mode is most.0377

First example, using this set of data, we are going to find the mean, median, and mode.0386

Mean, we are just going to add up all the numbers.0393

For mean, it doesn't if the numbers are in order because when you add, the order doesn't matter.0397

If I add 1 plus 2, it is going to be the same thing as 2 plus 1.0403

Here just add up all the numbers; 3 plus 5 plus 3 plus 8 plus 6 plus 10 plus 4.0407

Then we are going to divide that number by 1, 2, 3, 4, 5, 6, 7, seven numbers.0420

3 plus 5 is 8; plus 3 is 11.0431

That is 19; that is 25; that is 35; that is 39.0436

It is going to be 39; that is the sum; divided by 7.0444

You can either leave it like this as long as it doesn't simplify.0453

As long as there is no factors that goes into 39 and 7, you can just leave it as an improper fraction.0456

To change it to a mixed number, we ask ourselves how many times does 7 fit into 39?0467

I know 7 times 5 is 35; 7 times 6 is 42; that is too big.0474

My whole number is going to be 5 because 7 fits into 39 five times.0481

I have 4 leftovers; 4 over... keep the same denominator.0487

That will be our mean.0495

Again if you want to change this to a decimal instead, just do 39 divided by 7.0499

39 inside; divided by 7; put the decimal point at the end; bring it up.0506

I can add a 0 there if I want; I can add two 0s.0514

I can add three; it doesn't matter.0518

7 fits into 39 five times; that is 35; subtract it; I get 4.0520

Bring down this 0; 7 goes into 40 again five times; that is 35.0528

Subtract it; I get 5; I can bring down another 0.0538

7 goes into 50 seven times; that is 49.0544

Usually as long as you have one or two numbers behind the decimal point,0552

you can probably just stop there and write that as your answer.0556

Maybe like 5.57 or 5 point and then what you can do is maybe you can round this number.0559

This number is 5 or greater.0566

What you can do is you can round this number up to be 5.6.0571

That is the mean; I am just going to write 5.6.0578

The next one, median; remember the median, the keyword is middle.0588

Be careful here, the most common mistake for this one0595

is just finding the middle number from your data set.0599

Make sure you have to write the number in order from least to greatest.0605

My smallest number here I see is 3; I have another 3.0609

I have this is 4, then 5, 6, 8, and 10.0616

Make sure I have one, two, three, four, five, six, seven numbers.0628

The number in the middle, I can cross out the outside numbers one more time.0632

My median will be 5.0639

The last one, the mode is most; the mode is most.0645

What number do you see the most?--what number occurs the most?0652

That would be the 3 because 3 you see it twice.0657

The other numbers, you only see them once; 3 is going to be the mode.0662

The next example, same thing.0674

Find the mean, median, mode for the following set of data.0677

We have four numbers here for the mean; this is average.0683

We are going to add up all the numbers divided by however many numbers we have.0692

It is 15 plus 12 plus 19 and plus 10.0696

Divide that by... I have four numbers.0703

15 plus 12 is 27; write that there.0708

27 plus 19... 7 plus 9 is 16; bring up the 1.0715

I am going to write that 6 right here; 2, 3, 4.0722

27 plus 19 is 46; add the 10; you are going to get 56.0727

Divide that by 4; 56 and 4; I want to just divide it.0734

56 is going to go on the inside for 56 divided by 4.0748

4 goes into 5 one time; that gives you 4; subtract it.0754

Get 1 left over; bring down this number, 6.0762

4 goes into 16 four times; my mean is 14.0765

My median, that your middle number.0777

Let's write our numbers in order from least to greatest.0784

That is 12, then... forgot the 10; 10, 12, 15, 19.0787

The middle number, we have two middle numbers.0805

We are looking for the middle right in between 12 and 15.0811

We are going to find the average; we can add those two numbers together.0815

It is 12 plus 15 divided by 2; this becomes 27 divided by 2.0819

We can again change it to a decimal or leave it as a fraction.0830

27... I don't know why I wrote that.0835

27 divided by 2; 2 goes into 2, this first number, one time.0840

That is 2; subtract it; get 0; bring down the 7.0849

2 goes into 7 three times which is a 6; subtract it; get a 1.0854

From here, since I have a remainder, I can just go ahead and add my decimal point.0863

Bring it up; add the 0; bring down the 0.0867

2 goes into 10 five times; that gives me 10; I get no remainders.0872

My median here is going to be 13.5.0881

The last one is mode; the mode is the number that occurs the most.0890

15, we only see it once; 12 only once; 19 once; 10 once.0900

For the mode, we have none; we can just write none.0906

The next example, Sarah's test scores for the last five chapters are 90, 92, 86, 97, and 90.0913

Find the mode, mean, and median of her scores; let's start with the mode.0923

The mode, keyword most; we look at what number occurs the most.0931

The 90, we see 90 twice; my mode is going to be 90.0939

The next one is mean; mean is the average.0949

We are going to add up all the numbers.0959

90 plus 92 plus 86 plus 97 plus 90; all over... 1, 2, 3, 4, 5... 5.0961

Let's do this one right here; 90 plus 92 is... 2 and then 18.0981

Then I am going to add the next number, 86; plus 86.0991

You can do it this way.0995

Or you can just maybe list them all out and then add them up like that.0995

86; this is 8; 8 plus 8 is 16; that is 2.1001

We got this, this, this; now we have to add 97.1011

That is 15; this is 1 plus 9 is 10; plus 6 is 16; this is 3.1017

The last one, 90; this is 5; this is 15; this is 4.1028

When I add up all the numbers, it becomes 455.1040

Divided by... I have five numbers.1048

I know that 5 is going to go into this number evenly because it ends in a 5.1052

The number ends in a 5 or 0, then it is going to be divisible by 5.1057

455, let's divide it; 5 doesn't go into 4; 5 goes into 45 nine times.1063

That is going to give you 45; subtract it; get a 0.1076

Bring down the 5; 5 goes into 5 one time; that is a 5.1080

My answer is 91; that is my mean, the average; mean.1090

That means her test scores, if she scored these scores, her average is 91.1099

She is averaging pretty well; that is an A.1106

The last one is the median which is the middle.1112

The middle number, let's list our numbers in order from least to greatest.1120

The smallest number is 86.1125

Then we have 90; then 90 again; 92; and then 97.1130

Our median, our middle number, is 90.1144

The fourth example, the daily temperature for the last few days were 72, 70, 83, 75, 81, and 75.1153

Find the three measures of central tendency.1164

We have the mean, the median, then we have the mode.1166

First, mean; we know the keyword for the mean is average.1180

We have to add up all the numbers and divide it by however many numbers we have.1184

That is 70... 72 is our first one.1190

72 plus 70 plus 83 plus 75 plus 81 plus 75.1194

I have one, two, three, four, five, six numbers.1211

I am going to divide this sum by 6 because I have six numbers.1214

Let's add up the numbers; 72 plus 70.1222

I am just going to add up just like how I did before.1228

2 plus 0 is 2; this is 14; I am going to take this number.1232

I got this; I got that one; add this number, 83.1238

This is 5; this is 12; and then 2.1244

Add the 75; this is 10; 7; 9; 10; this is 3.1251

Add this one, 81; 1; 8; 3.1263

The last one is 75; this is 6.1271

8 plus 7 is 15; 3 plus 1 is 4; 456; 456 divided by 6.1278

Let's divide this number by 6; 56 divided by 6.1294

I know that 6 cannot fit into 4.1308

6 is going to fit into 45, this number here.1311

6, let's see; 6 times 6 is 36; 6 times 7 is 42.1316

6 times 8 is 48; we know that it is 7; this is 42.1321

If I subtract it, I get 3; bring down this number here, 6.1328

6 goes into 36 six times; that is 36; 0.1333

My mean here is 76; that is the average.1340

Let me just write this a little bit lower.1351

The next one is median; median, we know the keyword is middle.1356

We are going to look for the middle number after we list the numbers out in order from least to greatest.1366

The smallest number is 70; then let's see, 72.1373

Then 75; then again 75; then 81; and 83.1384

I have my six numbers; the middle number now.1401

I am going to cross out the last numbers; cross those out.1406

Then I have two numbers here.1411

Normally when you have two numbers, you are going to have to find the average between those two numbers.1414

You are going to have to find the middle number between those two.1419

You would add them; divided by 2.1423

But I know since they are both 75, the number in the middle of 75 will just be 75.1425

Median will just be 75.1436

It is the same number so then our median has to be that same number.1439

The last one, the mode, the keyword here is most.1446

What number from all the six numbers on our data, what number do we see the most?1451

That number would be 75.1458

It is the number that occurs the most; that is 75.1464

That is it for this lesson; thank you for watching Educator.com.1470

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