Question

8:21 AM * 75% Page D, Element X Mail - alberthe-be X ActionsX + 0 a berkeleycollege.instructure.com h ek This is a graded discussion: 1 point possible due Jan 26 21 DB-4 Chapter 3:Descriptive Statistics. The mean and the median are two types of measures of center. 1. Give a real-world example of when the median is preferred over the mean. Refer to the eText and resources in the course Materials folder. 2. Create your number collection, any 7-12 numbers of your choice. . Arrange them in order and find Median and Mean Calculate Sample Variance and Standard Deviation for your sample

Answer 1

1. We know that the outliers have significantly affected the mean and median is not affected by outliers. when the sample size is large and does not include outliers, the mean generally provides a better measure of central tendency. If there is one or two outliers then median is better. For example: suppose marks of 10 students of statistics Hons in a final exam are:

50,61,45,71,63,52,63,55,2,1.

Here 1 and 2 are outliers. Hence in this case median is more appropriate than mean.

Suppose 11 no.s between 7-12 are:

7,7,8,8,8,8,9,9,10,11,12

Median=(11+1)/2 i.e. 6th observation of the above ordered arrangement=8

$Mean=\frac{1}{11}\sum_{i=1}^{11}x_i=8.8182\\ Sample~variance=\frac{1}{10}\sum_{i=1}^{11}(x_i-\bar{x})^2=2.5636\\ Sample~Standard~deviation=\sqrt{\frac{1}{10}\sum_{i=1}^{11}(x_i-\bar{x})^2}=1.6011$