WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over stem and leaf plots.
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A stem and leaf plot is a way for you to organize your data so that it is easy to see.
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It lists them out in order from least to greatest.
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The stem of a stem and leaf plot is usually the tens digit.
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It is the number on the left.
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The leaf, red for the leaf, is the digit on the right which is the ones digit.
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Let's say I have a number 52.
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I am going to separate the number 52.
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I am going to separate the digits into a stem and then a leaf.
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The tens digit, the 5, I am going to make my stem.
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The ones digit, my 2, is going to be my leaf; stem and leaf.
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I am going to separate them by drawing a little line like that.
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All the stems are going to go on the left side.
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My leaves are going to go on the right side.
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That is a number.
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If I have these numbers here, I have 50, 52, and 55.
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The stem, the tens digit, is all the same.
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Since it is the same number, I am going to separate the stem and the leaves.
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But I only have to write the stem one time because it is the same stem.
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Then when I write my leaves, I am going to write the 0, the 2, and the 5.
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It becomes 0, just like I separated this number 52.
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Again because the stem is the same number,
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I am going to just put the leaf, that 2, right there next to the 0.
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Then again the next leaf, 5.
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This represents the tens digit and then all the ones digits.
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This is 50, 52, and then 55.
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That is how you do a stem and leaf plot.
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Using these numbers here, we are going to create a stem and leaf plot.
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The first stem, the smallest stem that I see is the 1.
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The smallest tens digit is the 1.
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I have a 2; that is another stem.
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I have a 3; I think that is it for my stems.
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I am going to list out my stems; stems and my leaves; stem and leaf.
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My stem, the smallest stem, 1; then 2; and then 3.
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I don't think I have any more stems; that is it for my stems.
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My leaves, the other side, I am going to write them out.
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Before you do this, it will be a little bit easier... you don't have to do this.
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But it is a little bit easier if you arrange your numbers in order from least to greatest.
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Let's just do that; my smallest number here is 11.
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Then it is 12; then 15; 18; let's see; then my twenties so it is 22; 25; 29.
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Next is 30; 32; I have another 32; 33; and 39.
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I have one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
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One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
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I have all my numbers.
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Now my stem, the 1, that is a tens digit; here is a tens digit.
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Then my 1, my leaf here is going to be a 1.
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This number here represents tens; ones; together, it becomes 11.
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My next one, because it is the same stem, I am going to write it under here, the same stem.
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The leaf here is 2 like that.
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You don't have to write commas; just leave a little space; 1, 2.
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Next is 5; the next leaf under the same stem is 8.
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That is it for my ones, my tens digit right here.
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Next is the 2, the 20s; that leaf is 2.
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The next leaf is 5; next leaf is 9.
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Moving on to the thirties, 3-0; 3-2; 3- another 2; 3-3; and 3-9.
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This is the stem and leaf plot that represents all of these numbers here.
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It represents my data; then I can see... what is my smallest number?
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My smallest number with the smallest stem and the smallest leaf together is going to be 11.
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My biggest number is going to be the biggest stem with the biggest leaf together is 39.
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To find the median here, it doesn't ask me to find the median.
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But I can find the median by eliminating because each leaf represents a number in the data.
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I can just go ahead and eliminate starting from this.
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This is the start; this is the last; the first and the last.
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I can just start eliminating until I get to a middle number, till I get to a middle leaf.
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Then I am going to use that stem and that leaf to create the median.
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We are going to do that in the next example, example three.
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Here we have a stem and leaf plot.
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We have to list all the numbers in order from least to greatest.
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It is like what we just did, except we are just going to do the opposite now.
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Instead of creating the stem and leaf plot with our data,
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we are going to use this to come up with our data, our list of numbers.
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The smallest number here, this stem with this leaf.
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This is the smallest leaf with the smallest stem, together makes 40.
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That is my smallest number, 40.
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My next is going to be 44; then 52; 55; 57; 58.
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Here this is listed out because all the stems from 4 to 7 have to be listed out.
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I don't have any leaves here with this stem.
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There is no number here that is in my data.
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I don't have sixties number.
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Then I just move on to 71; 73; and then 73.
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Notice, back to this 40, if I have a number 40, then I have to list out the 0 as my leaf.
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Here be careful not to represent this as 60 because there is no 0 here.
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Just because there is nothing there doesn't mean that you have a 60.
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There has to be a 0 in order for you to have a 60 in your data.
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This is it; these are all my numbers in this stem and leaf plot.
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For this one, some chapter test scores are given.
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Create a stem and leaf plot of the data.
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Then find the median and the mode.
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Again the first thing I want to do is list out my numbers in order from least to greatest.
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These are all chapter tests; the lowest score is 40.
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Then let's see, 48; 52; 67; 72; 83; and then... oh, I forgot 71.
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Let me go back to here, 72, 83; 71, 72, and then 83.
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After 83, 90... I forgot 79; back to 79.
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Where was I?--83; after 83 is 90; 91; 98; and 100.
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I have one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
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One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
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I have all my numbers in order from least to greatest.
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Now let's create our stem and leaf plot.
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My stems and my leaf, going to separate like that; going to use black for this.
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My smallest stem is a 4.
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My biggest stem is going to be this number here.
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Remember it is the numbers on the left.
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My ones digit is going to be my leaf.
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The remaining numbers to the left are going to be my stem.
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It is going to be my stem.
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Here I am going to separate this like that.
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10 is going to be my stem; the 0 is going to be my leaf.
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It is OK if you have more than one digit.
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If you have two or three digits as your stem, that is fine.
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4, 5, 6, 7, 8, 9, and 10; the leaf here is 0 and then 8.
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For the next one, the stem is 5; the leaf is 2.
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That is it for that.
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Stem is 6; leaf is 7; here, stem 7, leaf 1; and 2 and 3.
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This one's leaf is 3; for the nineties, 9-0; 9-1; 9-8.
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For the last one, 10-0.
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Those are all of the numbers represented in the stem and leaf plot.
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I need to find my median and my mode; here let's see.
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My median, because I know that the smallest stem with the smallest leaf is my smallest number in the data,
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and then my biggest stem with the biggest... this right here, the last leaf is going to be my biggest number,
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I know that I can start eliminating numbers from this right here and from the first and the last.
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If I keep doing that, eliminate this and eliminate that.
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The next one over is 48; the next one down from this is 98.
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Then this; then this; then this; then this; then 71; then 83.
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Then I have two numbers left in my data.
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The whole point of doing this right now is to find the median.
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I am trying to find the middle number.
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Median is always middle; that is the keyword.
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It has to be from order of least to greatest.
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You can look for the median from here because we already listed them out.
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But also be able to find the median from your stem and leaf plot.
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This is the start; small stem with the first leaf all the way down to the biggest stem with the last leaf.
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Start eliminating numbers until you get the middle; middle one or two middles.
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In this case, because we have an even number of numbers,
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we are going to have two numbers in the middle.
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To find the median, we have to find the average of those two numbers.
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For the median, it is going to be 2 plus the 9.
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We are going to find the middle number between 2 and 9.
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We are going to find the average or the mean between 2 and 9.
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I am going to add them together and divided by 2.
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2 plus 9 is 11; over 2.
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To change this to a decimal, you can change it to a fraction or a decimal.
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Remember that; 2, to change it to a mixed number...
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This is called an improper fraction where the top number is bigger than the bottom number.
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Let's change this to a mixed number.
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2 fits into 11 how many times?
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2 fits into 11 five times because that is going to make it a 10.
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It only fits into it five times; that is our whole number.
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How many leftovers do you have?--I have 1; over... keep that same denominator.
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It is going to be 5 and 1/2.
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To change this to a decimal, you are going to take the top number.
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Place it inside like that; 2 on the outside.
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You are going to put the decimal point at the end of that number.
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Bring it up; 2 fits into 11 five times.
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That gives us 10; subtract it; I get 1.
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I am going to add a 0 at the end of this; bring that down.
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2 goes into 10 five times; that gives us 10; subtract it; I get 0.
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Your median is going to be either 5 and 1/2 as a fraction or 5.5 as a decimal.
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It is just 5 and 1/2; that is the middle number between these two.
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That is our median.
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The mode, now mode, let's see.
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Do we see any leaves written out twice for the same stem?
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No, they are all different; I don't have a mode for this one.
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Let's say for example, if I have another 8 right here,
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then I know within the same stem, I have the same leaf written twice.
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That would mean that I would have 98 and 98 again.
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That would be my mode because remember the keyword for mode is most.
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We are looking for any repeats, any numbers that occur more than one time.
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Since I don't have any numbers that are repeating,
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any numbers that are occurring more than once, I have no mode.
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For mode, I am going to write none.
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That is it for this lesson; thank you for watching Educator.com.