Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was 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 ($x$): 0 1 2 3 4 5
No. of tosses ($f$): 38 144 342 287 164 25.

Given:

Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed the number of tosses during which 0,1,2,3,4 and 5 heads were obtained as shown in the table.

To do:

We have to find the mean number of heads per toss.

Solution:

Let the assumed mean $A=3$

Number of heads ($x_i$)	Number of tosses ($f_i$)	$d_i = x_i -A$ ($A = 3$)	$f_i \times\ d_i$
0	38	$-3$	$-114$
1	144	$-2$	$-288$
2	342	$-1$	$-342$
3-$A$	287	0	0
4	164	1	164
5	25	2	50
Total	$\sum{f_i}=1000$		$\sum{f_id_i}=-530$

We know that,

Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$

Therefore,

Mean $=3+(\frac{-530}{1000})$

$=3-0.53$

$=2.47$

The mean number of heads per toss is $2.47$.

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Updated on: 10-Oct-2022

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No. of heads per toss ($x$):	0	1	2	3	4	5
No. of tosses ($f$):	38	144	342	287	164	25.