Question

Which statement is not true about the data shown by the box plot below?

5 number summary: 23, 40, 55, 65, 79

A. The median of the data is 55.
B. The interquartile range is 55.
C. Three fourths of the data is less than 65.
D. The median of the upper half of the data is 65.
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Answer 1

B. The interquartile range is 55

Explanation:

the interquartile range is Q3 minus Q1, you would get 15 ,not 55. So B is the answer to your question

Answer 2

B. The interquartile range is 55.

Explanation:

In this problem, I refer to the right part of the box as the median of the upper half and the left part of the box as the median of the lower half.

The median of the data is going to be the middle line of the box and whisker plot. The middle line lies on 55, so the median is 55.

Choice A is true

The interquartile range is the right end of the box subtracted from the left end of the box. The right end of the box is 65. The left end of the box is 40. Subtracting the left end from the right end, we get 25.

Choice B is false

3/4 of the data will be where we see the right end of the box. The right end of the box is at 65. So, 3/4 of the data is less than 65.

Note: 1/4 of the data is less than the left side of the box at 40. 1/2 of the data is less than the median of the box which is at 55.

Choice C is true

The median of the upper half is the right end which is 65.

Note: The median of the lower half is 40.

Choice D is true