Find the mean deviation about median for the ...

NCERT Class XI Mathematics - Statistics - Solutions

Question : 11 of 34

Marks: +1, -0

Find the mean deviation about median for the following data :

Marks	0 - 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of girls	6	8	14	16	4	2

Solution:

Marks	Mid values $x_i$	$f_i$	c.f.	$\left\|x_i-27.86\right\|$	$f_i\left\|x_i-27.86\right\|$
0 - 10	5	6	6	22.86	137.16
10 - 20	15	8	14	12.86	102.88
20 - 30	25	14	28	2.86	40.04
30 - 40	35	16	44	7.14	114.24
40 - 50	45	4	48	17.14	68.56
50 - 60	55	2	50	27.14	54.28
		50			517.16

Here,

\frac{N}{2}

\frac{50}{2}

= 25

∴ Median class is 20 – 30

Median(M) = 20 +

\frac{25-14}{14}

× 10 = 20 + 7.86 = 27.86

∴ M.D. about median =

\frac{1}{N}\sum\limits^{\underset{i=1}{n}} f_i\left|x_i-M\right|

\frac{1}{50}

× 517.16 = 10.34

Go to Question:

Prev Question

Next Question