Question

An incomplete distribution is given below:

Variable:	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Frequency:	12	30	-	65	-	25	18

You are given that the median value is 46 and the total number of items is 230.

(i) Using the median formula fill up missing frequencies.

(ii) Calculate the AM of the completed distribution.

Answer 1

(i)

Class interval	Frequency	Cumulative frequency
10-20	12	12
20-30	30	42
30-40	x	42 + x
40-50	65	107 + x
50-60	y	107 + x + y
60-70	25	132 + x + y
70-80	18	150 + x + y
	N = 230

Given median = 46

Then, median class = 40 - 50

l = 40, h = 50 - 40 = 10, f = 65, F = 42 + x

Median `=l+((N/2)-F)/fxxh`

`rArr46=40+(115-(42+x))/65xx10`

`rArr46 - 40 = (115-42-x)/65xx10`

`rArr6=(73-x)/65=10`

`rArr(6xx65)/10=73-x`

`rArr390/10=73-x`

39 = 73 - x

x = 73 - 39

x = 34

Given N = 230

⇒ 12 + 30 + x + 65 + y + 25 + 18 = 230

⇒ 12 + 30 + 34 + 65 + y + 25 + 18 = 230

⇒ 184 + y = 230

⇒ y = 230 - 184

⇒ y = 46

 

(ii)

Class interval	Mid value(x)	Frequency(f)	fx
10-20	15	12	180
20-30	25	30	750
30-40	35	34	1190
40-50	45	65	2925
50-60	55	46	2530
60-70	65	25	1625
70-80	75	18	1350
		N = 230	`sumfx=10550`

Mean `=(sumfx)/N`

`=10550/230=45.87`