Question

Find the mean deviation about the mean for the following data: 6, 7, 10 , 12 , 13 , 4, 8, 12​

Answer 1

Answer:

Given Data is 6,7,10,12,13,α,12,16

Since Mean =10

M=

8

6+7+10+12+13+12+α+16

10=

8

76+α

10×8=76+α

80=76+α

α=4

Now , Mean Deviation from the mean

=

8

4+3+0+2+3+6+2+6

=

8

26

=3.25

Answer 2

Answer:

• 2.75

Solution:

Firstly we have to find out the mean (x) of given data.

$\bigstar\sf\red{\boxed{\sf Mean = \frac{\text{sum of all the terms}}{\text{Total no. of terms}}}}$

So,

$\sf Mean(x) = \dfrac{6+7+10 + 12 +13 + 4+ 8+12 }{8}\\\\\implies x=\dfrac{72}{8}\\\\\implies\boxed{\pink{\mathfrak{x=9}}}$

We have got the value of x(mean)

$\begin{array}{| c | c | c |}\bf \red{x_i }&\bf \red{x_i - \overline{x} }&\bf \red{|(x_i-\overline{x})|} \\ 6&6-9=-3 & 3 \\7 & 7-9=-2 & 2\\10 & 10-9=1 & 1\\12&12-9=3&3\\13&13-9 = 4&4\\4&4-9=-5&5\\8&8-9=-1&1\\12&12-9=3=3&3\\\end{array}$

• $\sum |x_i-\overline{x}| = 22$

Mean deviation about the mean =$\dfrac{\sum|x_i-\overline{x}|}{n}$

$\color{blue}\LARGE\mathfrak{Subsitute\;the\;values}$

$\textbf{Mean deviation about the mean}=\dfrac{22}{8}\\\\\textbf{Mean deviation about the mean}=2.75$

Therefore,

• Mean deviation about mean is 2.75