Chapter 11.2, Problem 1E

To determine

To find first quartile.

Answer to Problem 1E

Median of the lower half of the data set

Explanation of Solution

Given Information: first quartile of dataset.

Calculation:

The first quartile, denoted by  $Q_1$ , is the median of the  lower half  of the data set. This means that about 25% of the numbers in the data set lie below  Q₁  and about 75% lie above  $Q_1$ .

For example,

To find the first quartile of the data set $\{3,7,8,5,12,14,21,13,18\}$

First, we write data in increasing order: $\{3,5,7,8,12,13,14,18,21\}$

  

The median is 12.

So,

Therefore, the lower half of the data is: $\{3,5,7,8\}$

Now,

The first quartile,  $Q_1$ , is the median of $\{3,5,7,8\}$

So,

Since there is an even number of values, we need the mean of the middle two values to find the first quartile:

  .