Chapter 12.3, Problem 19P

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

4, 7, 5,9, 5,6; add 1

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 19P

Mean = 7

Median = 6.5

Mode = 6

Range = 5

Explanation of Solution

Given:

4 , 7 , 5 , 9 , 5 , 6 ; add 1

Calculation:

Perform the given operation to each data value:

5 , 8 , 6 , 10 , 6 , 7

Arrange the given data in ascending order :

5 , 6 , 6 , 7 , 8 , 10

Mean = $\frac{sum\text{ of all the entries}}{\text{total number of entries}}=\frac{5+6+6+7+8+10}{6}=\frac{42}{6}=7$

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 = $\frac{6+7}{2}=\frac{13}{2}=6.5$

Mode = The entry that appeares maximum number of times = 6

Range is the difference of the highest and lowest value of the data = 10-5 = 5