Question

Consider two data sets, A and B. The sets are identical except that the high value of data set A is three times greater than the high value of data set B.

(a) How do the medians of the two data sets compare?

It is impossible to know how the medians compare.

Both sets have the same median.   

Set A has a higher median.

Set B has a higher median.

(b) How do the means of the two data sets compare?

It is impossible to know how the means compare

.Both sets have the same mean.    

Set B has a higher mean.

Set A has a higher mean.

(c) How do the standard deviations of the two data sets compare?

Set A has a higher standard deviation.

Set B has a higher standard deviation.  

  It is impossible to know how the standard deviations compare

.Both sets have the same standard deviation.

(d) How do the box-and-whisker plots of the two data sets compare?

Both sets have identical whiskers on both sides

.Set A has a longer whisker on the right side.  

Set B has a longer whisker on the right side.

It is impossible to know how the box-and-whisker plots compare.

Set A has a longer whisker on the left side.

Set B has a longer whisker on the left side.

Answer 1

Let we consider two data sets, A and B as,

A   B
2   2
7   7
9   9
3   3
6   6
8   8
12   12
48   16
11   11
13   13

Then we use Minitab to solve the question.

Descriptive Statistics: A, B

Variable   Mean       StDev       Median
    A         11.90       13.19 8.50
    B          8.70    4.42   8.50

By considering above example we may came on conclusion that,

a) Both sets have the same median.

b) Set A has a higher mean.

c) Set A has a higher standard deviation.

d) Set A has longer whisker on the right side.