Chapter 10.1, Problem 18HP

To determine

To create a dataset with equal value of 25^th, 50^th and 75^th percentile.

Answer to Problem 18HP

Data set is 50, 60, 60, 60, 60, 60, 60, 80

Explanation of Solution

Given information:

Equal number of scores at the 25^th, 50^th and 75^th percentile.

Evaluation:

Considering the a data set,

50, 60, 60, 60, 60, 60, 60, 80

  $ValueOfX=\frac{percentile}{100}\times (n+1)$

For the value of 25^th percentile,

  $x=\frac{25}{100}\times (8+1)$

So,

  $x=\frac{25}{100}\times (9)$

On solving,

  $x=2.25$

On rounding of the value,

  $\approx 2$

On comparing the value to the table.

So, 25^th percentile is 60.

For the value of 50^th percentile,

  $x=\frac{50}{100}\times (8+1)$

So,

  $x=\frac{50}{100}\times (9)$

On solving,

  $x=4.5$

In this situation, taking the average of 4^th and 5^th value. Hence, substituting the value of 4^th and 5^th term,

  $=\frac{60+60}{2}$

So,

  $=\frac{120}{2}$

On solving,

  $=60$

Hence, 50^th percentile is 60.

For the value of 75^th percentile,

  $x=\frac{75}{100}\times (8+1)$

So,

  $x=\frac{75}{100}\times (9)$

On solving,

  $x=6.75$

On rounding of the values,

  $\approx 7$

Hence 75^th percentile is 60.

Comparing the 25^th, 50^th, and 75^th percentile.

Since, the value of 25^th, 50^th and 75^th percentile is equal. Therefore, the required data set is 50, 60, 60, 60, 60, 60, 60, 80.