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• ## Discussion

 1 answerLast reply by: Sandahl NelsonWed Jan 4, 2017 4:16 PMPost by Firebird wang on October 12, 2016Ms.Nelson, are you able to watch this two video which called Practice Test 2013 AP Statistics and Practice Test 2014 AP Statistics? I can't watch this two video, I dont know why. 3 answersLast reply by: Sandahl NelsonWed Jan 4, 2017 4:15 PMPost by Sandahl Nelson on February 25, 2016Hello,The population variance measures the variation from Mu (population mean), so we divide by N (capital N because it is the the whole population)The sample variance is used as an estimate for the population variance, but is actually the variation from X-bar (sample mean), so we divide n-1 (small n because it is the size of just the sample) to correct for the fact that we only use the variation around x-bar.In other words, we subtract 1 because the sample variance is an estimate of the variance of the population from which we draw the sample. Because the values in the sample will be (on average), closer to the sample mean than to the population mean, when we calculate variance using deviations from the sample mean it underestimates the variance of the population. Using n-1 instead of n as the divisor corrects for that. 1 answerLast reply by: Sandahl NelsonWed Jan 4, 2017 4:13 PMPost by Xiaming Jin on February 22, 2016I still don't understand what's the difference between the sample variance and the population variance, why sample variance should divide (n-1) instead of n??

### Summarizing Distributions of Univariate Data

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
• Objectives 0:10
• Measuring Center 0:42
• Median
• Mean
• Example: Find the Median and Mean 1:59
• Measuring Position 1:59
• Percentiles
• Quartiles
• Example: Find the Quartiles 8:58
• Range
• IQR
• Variance
• Example: Find the Measures of Spread 22:09
• Outliers 27:23
• Outliers
• Example: Outliers 29:05
• Boxplots 31:44
• 5-number Summary
• Example I: Boxplot 33:55
• Describe the Distribution 44:20
• SOCS: Shape, Outlier, Center, Spread