Question

Calculate the mean deviation about the median of the observation:

3011, 2780, 3020, 2354, 3541, 4150, 5000

Answer 1

Formula used for mean deviation:

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]

\[Here, \]

\[ d_i = x_i - M\]

 M = Median

 Arranging the data in ascending order:
2354, 2780, 3011, 3020, 3541, 4150, 5000

Here, median \[(M) = 3020\]  and n = 7. 

\[x_i\]	\[\left| d_i \right|\] \[\left| x_i - 3020 \right|\]
3011	9
2780	240
3020	0
2354	666
3541	521
4150	1130
5000	1980
Total	4546

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]

\[\Rightarrow MD = \frac{1}{7} \times 4546 = 649 . 42\]