What is the range of the data set?
23, 27, 42, 45, 49, 53, 62, 71, 76, 80
52.8
57
80
51
what is the interquartile range (iqr) of the data set?
23, 27, 42, 45, 49, 53, 62, 71, 76, 80
80
57
29
28
the box plots show students’ scores on a pre-test and a post-test.
which is the best estimate of the difference between the medians of the post-test and pre-test scores?
78.5
12
10
5

The range of the data set is 57.

The interquartile range (IQR) of the data set is 29.

The difference between the medians of the post-test and pre-test scores is 12.

Range is the difference between the largest and smallest number is a data set. It is a measure of variation.

Range = largest number - smallest number

80 - 23 = 57

In order to determine the the interquartile range, divide the numbers in the data set into two equal halves

First half = 23, 27, 42, 45, 49

Second half = 53, 62, 71, 76, 80

The second step is to determine the median of each half. The median is the number that is in the middle of a dataset.

Median of the first half = 42

Median of the second half = 71

The interquartile range is the difference between the two medians

71 - 42 = 29

A box plot is used to study the distribution of a dataset. The median can be determined  by tracing the line in the middle of box to the number line.

Median of the pre-test scores = 72

Median of the pre-test scores = 84

Difference = 84 - 72 = 12

To learn more about range, please check: link

Range is the difference between the highest number and the lowest number.

80 - 23 = 57

The answer is 57.

What is the interquartile range (IQR) of the data set?

23, 27, 42, 45, 49, 53, 62, 71, 76, 80

Find the middle of the data set, then find the middle of the lower half and the middle of the higher half and subtract.

The lower half is 23, 27, 42, 45, 49, the middle value of that is 42.

The upper half is 53, 62, 71, 76, 80, the middle value is 71.

The IQR is 71 - 42 = 29

The medians of the box plot are the vertical lines inside the colored box.

Orange = about 72

Blue = about 84

The difference = 84 - 72 = 12