Chapter 12.4, Problem 4P

Find the minimum, first quartile, median, third quartile, and maximum of each dataset.

5 8 9 7 11 4 9 4

To determine

Find minimum , first quartile , median , third quartile , and maximum of the given data set.

Answer to Problem 4P

Minimum = 4

First quartile = 4.5

Median = 7.5

Third quartile = 9

Maximum = 11

Explanation of Solution

Given:

5 , 8 , 9 , 7 , 11 , 4 , 9 , 4

Calculation:

Arrange the data in ascending order:

4 , 4 , 5 , 7 , 8 , 9 , 9 , 11

The minimum is 4.

The first quartile is the median of the lower half of the data set.

Since the total entries are 8, which is even , So, the lower half is the first $\frac{8}{2}=4$ entries.

So , the first quartile is $\frac{4+5}{2}=4.5$

Median = The mean of $\frac{8}{2}=4^{th}\&5^{th}$ entry = $\frac{7+8}{2}=7.5$

The third quartile is the median of the upper half of the data set.

Since the total entries are 8, which is even , So, the upper half is the last $\frac{8}{2}=4$ entries.

So , the third quartile is $\frac{9+9}{2}=9$

The maximum is 11