Question

A music website tracked the number of new users per day over 1 week. The number of new users for each day of the 7 days was 38, 43, 45, 50, 51, 56, 67.
a. What is the MAD of the number of new users per day? Round to the nearest tenth.

b. What does the value of the MAD represent? Explain

Answer 1

Part a)

MAD = median of absolute deviations

MAD = median of the set formed by : |each value - Median|

Then, first you have to find the median of the original set

The original set is (38, 43, 45, 50, 51, 56, 67)


The median is the value of the middle (when the set is sorte). This is 50.


Now calculate the absolute deviation of each data from the median of the data.

1) |38 - 50| = 12
2) |43 - 50| = 7
3) |45 - 50| = 5
4) |50 - 50| = 0
5) |51 - 50| = 1
6) |56 - 50| = 6
7) |67 - 50| = 17

Now arrange the asolute deviations in order

(0, 1, 5, 6, 7, 12, 17)

The median is the value of the middle: 6.

Then the MAD is 6.

Part b) MAD represents the median of the of the absolute deviations from the median of the data.