Question

The dot plot shows the number of books lent by a school library during a 10-day period.
What was the mean absolute deviation of the number of books?
F. 0
G.
H.
J.
1.04
1.96
..
23 24 25 26 27 28 29 30 31 32 33
2.19

Answer 1

The mean absolute deviation of the number of books is 1.84

How to determine the mean absolute deviation?

The dot plot of the number of books is in the attached figure.

From the figure, we have:

x      f

1       1

2      2

3      2

4      3

5      1

6     2

7     3

8     1

Start by calculating the mean using:

$\bar x= \frac{\sum fx}{\sum f}$

So, we have:

$\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}$

Evaluate the sum and products

$\bar x= \frac{69}{15}$

Divide

$\bar x= 4.6$

The mean absolute deviation is then calculated as:

$|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}$

So, we have:

$|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}$

Evaluate the absolute difference

$|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}$

Evaluate the sum of products

$|\bar x|= \frac{27.6}{15}$

Divide

$|\bar x|= 1.84$

Hence, the mean absolute deviation of the number of books is 1.84

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