Chapter 11, Problem 11CT

Solution

To Calculate: Quartile 1 and Quartile 3 for the given set of values.

The Quartile 1 and Quartile 3 of the given data set are 42 and 69 respectively.

Given:

The data set is shown below

  $36,38,42,47,51,56,62,69,70,74$

Concept:

Quartile 1 of a data set divides the lower 25% of the data and the upper 75% of the data in a data distribution or it is the median of the first half of the data distribution. Quartile 3 of a data set divides the upper 25% of the data and lower 75% of the data in a data distribution or it is the median of the second half of the data distribution.

Calculation:

Given data set has a total of 10 data values. Considering the first half of the data set, the first five data points as shown below

  $36,38,42,47,51$

there are a total of five data values and the middle value of the first half of the data distribution is the third value in the above data distribution “42”. Thus $\text{Quartile 1}=42$

Considering the second half of the data set, the first five data points as shown below

  $56,62,69,70,74$

there are a total of five data values and the middle value of the second half of the data distribution is the third value in the above data distribution “69”. Thus $\text{Quartile 3}=69$Thus $Q_1=42,Q_3=69$