Question

9. Income per 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800day inNumber 4 8of persons104

Answer 1

The given data is:

Income per day	Number of persons
0-100	4
100-200	8
200-300	9
300-400	10
400-500	7
500-600	5
600-700	4
700-800	3

Create the following table:

Income per day	Number of persons, f i	Midpoint, x i	f i x i	| x i − x ¯ |	f i | x i − x ¯ |
0-100	4	50	200	308	1232
100-200	8	150	1200	208	1664
200-300	9	250	2250	108	972
300-400	10	350	3500	8	80
400-500	7	450	3150	92	644
500-600	5	550	2750	192	960
600-700	4	650	2600	292	1168
700-800	3	750	2250	392	1176
	∑ i=1 n f i =50		∑ i=1 n f i x i =17900		∑ i=1 n f i | x i − x ¯ | =7896

The formula to calculate the mean when continuous frequency is given is,

x ¯ = ∑ i=1 n x i f i ∑ i=1 n f i x ¯ = 1 N ∑ i=1 n x i f i

Where, N is the sum of frequency.

Substitute 50 for N and 17900 for ∑ i=1 n x i f i in equation (1).

x ¯ = 17900 50 =358

Therefore, the mean of the given data is 358.

The formula to calculate the mean deviation about the mean is,

M.D= ∑ i=1 n f i | x i − x ¯ | ∑ i=1 n f i M.D= 1 N ∑ i=1 n f i | x i − x ¯ |

Substitute 50 for N and 7896for ∑ i=1 n f i | x i − x ¯ | in equation (2).

M.D.= 7896 50 =157.92

Therefore, the mean deviation of the given data is 157.92.