Calculate the mean deviation about median ...

NCERT Class XI Mathematics - Statistics - Solutions

Question : 12 of 34

Marks: +1, -0

Calculate the mean deviation about median age for the age distribution of 100 persons given below :

Age	16 – 20	21 – 25	26 – 30	31 – 35	36 – 40	41 – 45	46 – 50	51 – 55
Number	5	6	12	14	26	12	16	9

[Hint : Convert the given data into continuous frequency distribution by subtracting 0.5 from lower limit and adding 0.5 to the upper limit of each class interval]

Solution:

Age	Modified class	Mid values $x_i$	$f_i$	c.f.	$\left\|x_i - 38\right\|$	$f_i\left\|x_i-38\right\|$
16 - 20	15.5-20.5	18	5	5	20	100
21 - 25	20.5 - 25.5	23	6	11	15	90
26 - 30	25.5 - 30.5	28	12	23	10	120
31 - 35	30.5 - 35.5	33	14	37	5	70
36 - 40	35.5 - 40.5	38	26	63	0	0
41 - 45	40.5 - 45.5	43	12	75	5	60
46 - 50	45.5-50.5	48	16	91	10	160
51 - 55	50.5 - 55.5	53	9	100	15	135
			100			735

Here,

\frac{N}{2}

\frac{100}{2}

= 50

∴ Median class is 35.5 - 40.5

Median(M) = 35.5 +

\frac{50-37}{26}

× 5 = 35.5 + 2.5 = 38

Mean deviation about median =

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

\frac{735}{100}

= 7.35

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