Chapter 12.3, Problem 18P

The heights of a painter’s ladders are 12 ft, 8 ft, 4 ft, 3 ft, and 6 ft. What are the mean, median, mode, and range of the ladder heights?

To determine

Find mean , median , mode , and range of the ladder heights.

Answer to Problem 18P

Mean = 6.6

Median = 6

Mode = no mode

Range = 9

Explanation of Solution

Given:

The heights of a painter’s ladders are 12 ft. , 8 ft. ,4 ft. ,3 ft. , and 6 ft.

Calculation:

Arrange the given data in ascending order :

3 , 4 , 6 , 8 , 12

Mean = $\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{3+4+6+8+12}{5}=\frac{33}{5}=6.6$

Median = The middle entry of the data( since there are 5 entries , which is odd) = $\frac{number\text{ of entries +1}}{2}=\frac{5+1}{2}=3^{rd}$

So, median is 3^rd entry = 6

Mode = The entry that appeares maximum number of times = Here all the values appear only once .So, no mode.

Range is the difference of the highest and lowest value of the data = 12-3 = 9