Chapter 13, Problem 6MCQ

To determine

The interquartile range of given data

Answer to Problem 6MCQ

Option A. 13

Explanation of Solution

Given:

The given data is:

45, 57, 55, 42, 48, 21, 39, 62, 45, 51

Calculation:

To find the interquartile range of the given data:

Order the data from least to greatest

21, 39, 42, 45, 45, 48, 51, 55, 57, 62

Now, find the median of the ordered data:

As the number of data items are 10 (even), the median will be 5^th data value + 6^th data value/2.

So, Median will be:

  $\begin{array}{l}=\frac{\left(45+48\right)}{2}\\ =\frac{93}{2}\\ =46.5\end{array}$

Now, we will calculate the median of lower data set and the upper data set.

Divide the given data set having 10 data items into two data sets with 5 data items each.

So, lower data set will be:

21, 39, 42, 45, 45

And the upper data set will be:

48, 51, 55, 57, 62

We will calculate the median of both these data sets now.

Median of lower data set:

21, 39, 42, 45, 45

Median will be the exact middle value as the number of terms are 5 (odd).

So, Median of lower data set = 42

Median of upper data set:

48, 51, 55, 57, 62

Median will be the exact middle value as the number of terms are 5 (odd).

So, Median of upper data set = 55

Lastly, subtract the median of lower data set from the median of upper data set to get the Interquartile range.

Median of lower data set = 42

Median of upper data set = 55

Interquartile Range = 55 - 42

Interquartile Range = 13

So, Option A. 13 is the correct answer.