Question

Using the following data, calculate the mean absolute deviation:

Answer 1

Answer:

The mean absolute deviation of first data is $2.54$

and for second data is $2.115$

Step-by-step explanation:

Mean of  data $x_1,x_2,x_3,x_4,...x_{n}$ is calculated as:

$mean=\frac{x_1+x_2+x_3+x_4+...+x_n}{n}$

and mean absolute deviation is calculated as $\sqrt{mean}$

The given first data : 10 7 1 6 7 9 8 10 2 5

$mean=\frac{x_1+x_2+x_3+x_4+...+x_n}{n}$

$mean=\frac{10+7+1+6+7+9+8+10+2+5}{10}$

$mean=6.5$

mean absolute deviation $\sqrt{6.5}=2.54$

The given first data : 2   2.4   6.5   7

$mean=\frac{x_1+x_2+x_3+x_4+...+x_n}{n}$

$mean=\frac{2+2.4+6.5+7}{4}$

$mean=\frac{17.9}{4}$

$mean=4.475$

mean absolute deviation $\sqrt{4.475}=2.115$

Therefore, the mean absolute deviation of first data is $2.54$

and for second data is $2.115$

Answer 2

First set of data:
Mean - 6.5
Absolute deviation - 2.4

Second set of data:
Mean - 4.475
Absolute deviation - 2.275