Chapter 10.3, Problem 25PFA

To determine

To calculate upper and lower quartiles.

Answer to Problem 25PFA

Lower quartile is 20.5 and Upper quartile is 50.5

Explanation of Solution

Given information:

Data is 37, 62, 10, 13, 54, 44, 47, 28, 30.

Formula used: Lower quartile is,

  $Q1=(n+1)\times \frac{1}{4}$

Upper quartile is,

  $Q3=(n+1)\times \frac{3}{4}$

Re-arranging the data in an ascending order,

10, 13, 28, 30, 37, 44, 47, 54, 62

For lower quartile substituting the values,

  $Q1=(9+1)\times \frac{1}{4}$

So,

  $Q1=(10)\times \frac{1}{4}$

On solving,

  $Q1=2.5$

Hence, adding 2^nd and 3^rd to get the answer,

  $Q1=\frac{13+28}{2}$

So,

  $Q1=\frac{41}{2}$

On solving,

  $Q1=20.5$

For upper quartile substituting the value,

  $Q3=(9+1)\times \frac{3}{4}$

So,

  $Q3=(10)\times \frac{3}{4}$

On solving,

  $Q3=7.5$

Hence, adding 7^th and 8^th to get the answer,

  $Q3=\frac{47+54}{2}$

So,

  $Q3=\frac{101}{2}$

On solving,

  $Q3=50.5$

Hence, Lower quartile is 20.5 and Upper quartile is 50.5