Chapter 13.3, Problem 18STP

To determine

To find: The inter-quartile range

Answer to Problem 18STP

Inter-quartile range is 4. Therefore, option H, G, J are incorrect.

Hence option F.4 is correct.

Explanation of Solution

Given:

This is the given information:

The database in ascending order is as follows.

29, 31, 31, 32, 33, 33, 34, 34, 34, 34, 35, 36, 37, 39,39

Here n total number of observations are in dataset

Calculate Lower Quartile (LQ).

Lower Quartile (LQ) is the value of observation in dataset arranged in ascending order.

Lower Quartile (LQ) the value of observation

The value of observation

The value of observation is 32.

3. Here n=total number of observation in dataset=15

Calculate Upper Quartile (UP).

Upper Quartile (UP) is the value of ${\left(\frac{3(n+1)}{4}\right)}^{th}$ observation in dataset arranged in ascending order.

Upper Quartile (UP)= The value of ${\left(\frac{3(15+1)}{4}\right)}^{th}$ observation

=The value of observation

=The value of ${12}^{\text{th}}$ observation

  $=36$

4.Calculate Inter-quartile range (IQR)

Inter-quartile range (IQR) = Upper Quartile (UQ) − Lower Quartile (LQ)

  $\begin{array}{l}=36-32\hfill \\ =4\hfill \end{array}$

5. Inter-quartile range is 4. Therefore, option H, G, J are incorrect.

6. Hence option F.4 is correct.