Question

Find the mean of the following distribution :

Height (In cm)	Less than 75	Less than 100	Less than 125	Less than 150	Less than 175	Less than 200
No. of students	5	11	14	18	21	28
Height (in cm)	Less than 225	Less than 250	Less than 275	Less than 300
No. of students	33	37	45	50

Answer 1

Class Interval Height (in cm)	Frequency (fi)	xi	u = (xi - a)/h	fiui
50 - 75	5	62.5	-5	-25
75 - 100	6	87.5	-4	-24
100 - 125	3	112.5	-3	-9
125 - 150	4	137.5	-2	-8
150 - 175	3	162.5	-1	-3
175 - 200	7	187.5 = a	0	0
200 - 225	5	212.5	1	5
225 - 250	4	237.5	2	8
250 - 275	8	262.5	3	24
275 - 300	5	287.5	4	20
	Σfi = 50			Σfiui = -12

Σf_iu_i = -12

N = 50

h = 25

Mean = \(a +\frac{\sum f_iu_i}N \times h\)

\(= 187.5 + \frac{-12}{50} \times 25\)

\(= 187.5 -6\)

\(= 181 .5\)

Answer 2

                = 187.5 - 6 = 181.5 

Comments

How did you get 62.5?

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Upper limit + lower limit/2 = xi
= 75+50/2
= 125/2
= 62.5