Indira makes a box-and-whisker plot of her data. she finds that the distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value. which is most likely true? 1.the mean is greater than the median because the data is skewed to the right. 2.the mean is greater than the median because the data is skewed to the left. 3.the mean is less than the median because the data is skewed to the right. 4.the mean is less than the median because the data is skewed to the left.

Solution:

Indira is saying that,  distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value.

Consider the Data set

0,2,3,6,8,9,10,11

Mean=

Median =As number of terms in data set are even, so median will be mean of two mid values.

First Quartile(A)  =  middle number between the smallest number and the median of the data set.

A= 3

Second Quartile(M) = median of the data.

M= 7

Third Quartile(B) = middle value between the median and the highest value of the data set.

B=9

Distance between minimum value and first Quartile= 3-0=3

Distance between the third Quartile and the maximum =11-9=2

As,Sum of difference between median and values left to Median of data set > Sum of difference between median and values Right to Median of data set

So, if you will draw the  graph by plotting the points in two dimensional coordinate plane, you will find that, mean is less than the median because the data is skewed to the left, the reason being values in data set are more Scattered in left of the Median than to the Right of median.

Option 4.The mean is less than the median because the data is skewed to the left, Describes the situation represented in Statistical terms .