Question

The high temperatures at a park for 10 days are 40, 42, 41, 41, 43, 43, 44, 45, 44, and 45 degrees Fahrenheit. What is the interquartile range of the data?

Answer 1

The interquartile range of the data is 3.

Explanation:

Here, the given data is,

40, 42, 41, 41, 43, 43, 44, 45, 44, 45,

Step 1 : The ascending order of the data,

40, 41, 41, 42, 43, 43, 44, 44, 45, 45,

Step 2 : Median of the data,

40, 41, 41, 42, 43, 43, 44, 44, 45, 45

Step 3 : Make a mark in the center of the data,

40, 41, 41, 42, 43, | 43, 44, 44, 45, 45

Step 4 : Make lower half and upper half of the data,

(40, 41, 41, 42, 43) | (43, 44, 44, 45, 45)

Step 5 : Median of lower half,

`Q_1` = 41,

Median of upper half,

`Q_3` = 44

Step 6 : Thus, the interquartile range of the data =
`Q_3-Q_1`

= 44 - 41

= 3

Answer 2

Range in a distribution is the difference between the smallest and the largest value in a distribution. Interquartile range is the difference between the upper quartile and the lower quartile in a distribution.
In an ungrouped data , the first step is to arrange the values in ascending order;
40,41,41,42,43,43,44,44,45,45
The lower quartile is 41 while the upper quartile is 44
Thus the interquartile range is 3 (44-41)