Find the Five Number Summary 12 , 15 , 45 , 65 , 78

$12$ ,

$15$ ,

$45$ ,

$65$ ,

$78$

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.

$12, 15, 45, 65, 78$

Step 3

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

$12$

Step 4

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

$78$

Step 5

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

$45$

Step 6

Find the first quartile by finding the median of the set of values to the left of the median.

The lower half of data is the set below the median.

$12, 15$

The median for the lower half of data

$12, 15$ is the lower or first quartile. In this case, the first quartile is

$13.5$ .

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{12 + 15}{2}$

Remove parentheses.

$\frac{12 + 15}{2}$

Add

$12$ and

$15$ .

$\frac{27}{2}$

Convert the median

$\frac{27}{2}$ to decimal.

$13.5$

Step 7

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.

$65, 78$

The median for the upper half of data

$65, 78$ is the upper or third quartile. In this case, the third quartile is

$71.5$ .

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$\frac{65 + 78}{2}$

Remove parentheses.

$\frac{65 + 78}{2}$

Add

$65$ and

$78$ .

$\frac{143}{2}$

Convert the median

$\frac{143}{2}$ to decimal.

$71.5$

Step 8

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

$Min = 12$

$Max = 78$

$M = 45$

$Q_{1} = 13.5$

$Q_{3} = 71.5$

Find the Five Number Summary 12 , 15 , 45 , 65 , 78

Related Questions