Find the Five Number Summary 64 , 69 , 69 , 69 , 71 , 74 , 74

$64$ , $69$ , $69$ , $69$ , $71$ , $74$ , $74$

Step 1

The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the following statistics:

1. Minimum (Min) - the smallest observation

2. Maximum (Max) - the largest observation

3. Median $M$ - the middle term

4. First Quartile $Q_{1}$ - the middle term of values below the median

5. Third Quartile $Q_{3}$ - the middle term of values above the median

Step 2

Arrange the terms in ascending order.

$64, 69, 69, 69, 71, 74, 74$

Step 3

The minimum value is the smallest value in the arranged data set.

$64$

Step 4

The maximum value is the largest value in the arranged data set.

$74$

Step 5

The median is the middle term in the arranged data set.

$69$

Step 6

Find the third quartile by finding the median of the set of values to the right of the median.

The upper half of data is the set above the median.

$71, 74, 74$

The median is the middle term in the arranged data set.

$74$

Step 7

The five most important sample values are sample minimum, sample maximum, median, lower quartile, and upper quartile.

$Min = 64$

$Max = 74$

$M = 69$

$Q_{1} = 69$

$Q_{3} = 74$