Question

10 14 18 24 28 30f 2 47 12 8 434. x 6

Answer 1

The given data is:

x i	6	10	14	18	24	28	30
f i	2	4	7	12	8	4	3

Now, make a table by using discrete frequency.

x i	f i	f i x i	x i − x ¯	( x i − x ¯ ) 2	f i ( x i − x ¯ ) 2
6	2	12	−13	169	338
10	4	40	−9	81	324
14	7	98	−5	25	175
18	12	216	−1	1	12
24	8	192	5	25	200
28	4	112	9	81	324
30	3	90	11	121	363
	∑ i=1 n f i =40	∑ i=1 n x i f i =760			∑ i=1 n f i ( x i − x ¯ ) 2 =1736

The formula to calculate the mean when discrete 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 (1)

Where, N is the sum of discrete frequency.

Substitute 40 for N and 760 for ∑ i=1 n x i f i in equation (1).

x ¯ = 760 40 =19

Therefore, the mean of the given data is 19.

The formula to calculate the variance is,

σ 2 = 1 N ∑ i=1 n f i ( x i − x ¯ ) 2 (2)

Substitute 40 for N and 1736 for ∑ i=1 n f i ( x i − x ¯ ) 2 in equation (2).

σ 2 = 1736 40 =43.4

Thus, the variance of the given data is 43.4.