Chapter 12.3, Problem 24P

Find the mean, median., mode, and range of each data set after you perform the given operation on each data value.

3.2, 4.4, 6, 7.8, 3, 2; subtract -4

To determine

Find mean , median , mode , and range of the given data after performing the given operation first to each data value.

Answer to Problem 24P

Mean = 8.4

Median = 7.8

Mode = no mode

Range = 5.8

Explanation of Solution

Given:

3.2 , 4.4 , 6 , 7.8 , 3 , 2 ; subtract -4

Calculation:

Perform the given operation to each data value:

7.2 , 8.4 , 10 , 11.8 , 7 , 6

Arrange the given data in ascending order :

6 , 7 , 7.2 , 8.4 , 10 , 11.8

Mean = $\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{6+7+7.2+8.4+10+11.8}{6}=\frac{50.4}{6}=8.4$

Median = The $\frac{6}{2}=3^{rd}$ and $$ 4^th data value ( since there are 6 entries , which is even) are the middle values , so the median = $\frac{7.2+8.4}{2}=\frac{15.6}{2}=7.8$

Mode = The entry that appeares maximum number of times = since all the data values occur only once , so , there is no mode.

Range is the difference of the highest and lowest value of the data =11.8 − 6 = 5.8