Question

95-105 105-115 115-125 125-135 135-145 145-15510. Height9in cmsNumber ofboys1326301210

Answer 1

The given data is:

Height in cms	Number of boys
95-105	9
105-115	13
115-125	26
125-135	30
135-145	12
145-155	10

Creating a table as follows:

Height in cms	Number of boys, f i	Midpoint, x i	f i x i	| x i − x ¯ |	f i | x i − x ¯ |
95-105	9	100	900	25.3	227.7
105-115	13	110	1430	15.3	198.9
115-125	26	120	3120	5.3	137.8
125-135	30	130	3900	4.7	141
135-145	12	140	1680	14.7	176.4
145-155	10	150	1500	24.7	247
	∑ i=1 n f i =100		∑ i=1 n f i x i =12530		∑ i=1 n f i | x i − x ¯ | =1128.8

The formula to calculate the mean is given as,

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 100 for N and 12530 for ∑ i=1 n x i f i in the above equation

x ¯ = 12530 100 =125.3

Therefore, the mean of the given data is 125.3.

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 100 for N and 1128.8for ∑ i=1 n f i | x i − x ¯ | in the above equation

M.D.= 1128.8 100 =11.28

Therefore, the mean deviation of the given data is 11.28.