Find the mean deviation about the mean for the data. \[4\], \[7\], \[8\], \[9\], \[10\], \[12\], \[13\], \[17\] - Noon Academy

Find the mean deviation about the mean for the data.

$4$

,

$7$

,

$8$

,

$9$

,

$10$

,

$12$

,

$13$

,

$17$

Class 11 | Exercise 15.1 | Maths | NCERT | Statistics

Find the mean deviation about the mean for the data.

$4$

,

$7$

,

$8$

,

$9$

,

$10$

,

$12$

,

$13$

,

$17$

Solution:-

Given data

$4$

,

$7$

,

$8$

,

$9$

,

$10$

,

$12$

,

$13$

,

$17$

To find mean deviation, first we have to find mean

$(\overline{x})$

$\overline{x}=\frac{1}{8}\sum\limits_{i=1}^{8}{{{x}_{i}}}=\frac{80}{8}=10$

Determine the respective values of the deviations from mean,

i.e.,

${{x}_{i}}-\overline{x}$

are,

$10-4=6$

,

$10-7=3$

,

$10-8=2$

,

$10-9=1$

,

$10-10=0$

,

$10-12=-2$

,

$10-13=-3$

,

$10-17=-7$

The deviations are

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

Therefore, the absolute values of the deviations,

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

Therefore,

$\sum\limits_{i=1}^{8}{\left| {{x}_{i}}-\overline{x} \right|}=24$

We know that Mean deviation = sum of deviations/ number of observations

=

$24/8$

=

$3$

Hence, the mean deviation for the given data is

$3$

.

i

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