Question

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss	No. of tosses
0	38
1	144
2	342
3	287
4	164
5	25
Total	1000

Answer 1

No. of heads per toss	No. of tosses	fx
0	38	0
1	144	144
2	342	684
3	287	861
4	164	656
5	25	125
	N = 1000	`sum`fx = 2470

Mean number of heads per toss `=(sumfx)/N`

`=2470/1000=2.47`

∴ Mean = 2.47

Answer 2

Let the assumed mean (A) = 2

No. of heads per toss (x1)	No. of intervals (f1)	u1 = x1 - A (A = 2)	f1u1
0	38	-2	-76
1	144	-1	+44
2	342	0	0
3	287	1	287
4	164	2	328
5	25	3	75
	N = 1000		`sumf_1u_1=470`

Mean number of per toss `=A+(sumf_1u_1)/N`

`=2+470/1000`

= 2 + 0.47

= 2.47