Question

Following is the distribution of I.Q. of loo students. Find the median I.Q.

I.Q.:	55 - 64	65 - 74	75 - 84	85 - 94	95 - 104	105 - 114	115 - 124	125 - 134	135 - 144
No of Students:	1	2	9	22	33	22	8	2	1

Answer 1

Class interval(inclusive)	Class interval(exclusive)	Frequency	Cumulative frequency(c.f)
55 - 64	54.5 - 64.5	1	1
65 - 74	64.5 - 74.5	2	3
75 - 84	74.5 - 84.5	9	12
85 - 94	84.5 - 94.5	22	34
95 - 104	94.5 - 104.5	33	67
105 - 114	104.5 - 114.5	22	89
115 - 124	114.5 - 124.5	8	97
125 - 134	124.5 - 134.5	2	99
135 - 144	134.5 - 144.5	1	100
		N = 100

Here, N = 100

So, N/2 = 50

Thus, the cumulative frequency just greater than 50 is 67 and the corresponding class is 94.5−104.5.

Therefore, 94.5−104.5 is the median class.

Here, l = 94.5, f = 33, F = 34 and h = 10

We know that,

Median `=l+{(N/2-F)/f}xxh`

`=94.5+((50-34)/33)xx10`

`=94.5+160/33`

= 94.5 + 4.85

= 99.35