Question

Vivian surveyed bicyclists in her community to see the average number of miles they biked per day. Her results are shown below. 7, 10, 13, 4, 12, 21, 10, 3 What is the MAD of her data set? What does this tell you about the number of miles biked each day by the bicyclists?

Answer 1

Answer:

MAD of her data set is 4.

Step-by-step explanation:

Vivian surveyed bicyclists in her community to see the average number of miles they biked per day.

The data set is given below :

7, 10, 13, 4, 12, 21, 10, 3

$mean=\frac{\text{Sum of data set}}{\text{number of values}}$

$=\frac{(7+10+13+4+12+21+10+3)}{8}$

$=\frac{80}{8}$

= 10

$MAD=\frac{\sum |A_1-f_1|}{n}$

              Data point          Distance from mean

                                             

1                  7                           7 - 10   =     | -3 |     = 3

2.                10                         10 - 10  =     | 0 |       = 0

3.                13                          13 - 10  =     | 3 |     = 3

4.                4                           4 - 10    =    | -6 |    = 6

5.               12                          12 - 10   =    | 2 |     = 2

6.               21                          21 - 10   =    | 11 |   = 11

7.               10                          10 - 10   =    | 0 |     = 0

8.               3                            3 - 10   =    | -7 |   = 7

                                               

Adding the distance = 3 + 0 + 3 + 6 + 2 + 11 + 0 + 7 = 32

MAD = $\frac{32}{8}$ = 4

MAD of her data set is 4.

Mean Absolute Deviation of this data tells about the variation of 4 miles biked each day by the bicyclists.