Find the mean deviation about the mean for the data
$4, 7, 8, 9, 10, 12, 13, 17$

Question

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Answer 1

The given data is $4, 7, 8, 9, 10, 12, 13, 17$
Mean of the data $\overset{x}{ˉ} = \frac{4 + 7 + 8 + 9 + 1 0 + 1 2 + 1 3 + 1 7}{8} = \frac{8 0}{8} = 10$

The deviations of the respective observations from the mean $\overset{x}{ˉ} i . e . x_{i} - \overset{x}{ˉ},$ are $- 6, - 3, - 2, - 1, 0, 2, 3, 7$ .

The absolute values of the deviations i.e. $∣ x_{i} - \overset{x}{ˉ} ∣$ , are $6, 3, 2, 1, 0, 2, 3, 7$ .

The required mean deviation about the mean is
$M . D . = \frac{\sum _{i = 1}^{8} ∣ x _{i} - x ˉ ∣}{8}$

$M . D . = \frac{6 + 3 + 2 + 1 + 0 + 2 + 3 + 7}{8} = \frac{2 4}{8} = 3$

Answer 2

The given data is

4, 7, 8, 9, 10, 12, 13, 17

Mean of the data

\overset{x}{ˉ} = \frac{4 + 7 + 8 + 9 + 1 0 + 1 2 + 1 3 + 1 7}{8} = \frac{8 0}{8} = 10

The deviations of the respective observations from the mean

\overset{x}{ˉ} i . e . x_{i} - \overset{x}{ˉ},

are

- 6, - 3, - 2, - 1, 0, 2, 3, 7

.

The absolute values of the deviations i.e.

∣ x_{i} - \overset{x}{ˉ} ∣

, are

6, 3, 2, 1, 0, 2, 3, 7

.

The required mean deviation about the mean is

M . D . = \frac{\sum _{i = 1}^{8} ∣ x _{i} - x ˉ ∣}{8}

M . D . = \frac{6 + 3 + 2 + 1 + 0 + 2 + 3 + 7}{8} = \frac{2 4}{8} = 3

$x_{i}$	5	10	15	20	25
$f_{i}$	7	4	6	3	5

$X_{i}$	10	30	50	70	90
$f_{i}$	4	24	28	16	8