Question

A sample of 20 Ohio University students were randomly selected and asked, “How many phone calls did you receive last night?” The numbers below are their responses.

1  2  0  2  4  2  3  4  5  3 0  4  5  6  3  10  7  6  7  11

Compute the IQR of the distribution.

Answers:

a. 6

b. 3

c. 4

d. 2

Answer 1

Solution:-
=> option c. 4

Explanation

The interquartile range is the difference between the third and first quartiles.

The third quartile is 6.

The first quartile is 2.

The interquartile range = 6 - 2 = 4.

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Explanation

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

0   0   1   2   2   2   3   3   3   4   4   4   5   5   6   6   7   7   10   11   

So, the bottom half is

0   0   1   2   2   2   3   3   3   4   

The median of these numbers is 2.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

0   0   1   2   2   2   3   3   3   4   4   4   5   5   6   6   7   7   10   11   

So, the upper half is

4   4   5   5   6   6   7   7   10   11   

The median of these numbers is 6.