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.

Question

Philoid · Accepted Answer

(i)

Class interval	Frequency	Cumulative frequency
10-20	12	12
20-30	30	42
30-40	X	42 + x (F)
40-50	65 (f)	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

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

Median = l +

46 = 40 + * 10

= 73 – x

39 = 73 – x

x = 73 – 39

x = 34

Given, N = 230

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

= 184 + y = 230

= y = 230 – 184 = 46

(ii)

Class interval	Mid – value	Frequency	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	∑fx = 10550

Mean =

= = 45.87

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

An incomplete distribution is given below:Variable:10-2020-3030-4040-5050-6060-7070-80Frequency:1230-65-2518You 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.