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

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Best answer

Let the assumed mean (A) = 2

 No. of heads per toss (xi)  No. of intervals (fi)  Ui = xi - A = xi - 2 fiui
 0 38 -2 -76
1 144 -1 -144
2 342 0 0
3 287 1 287
4 164 2 328
5 25 3 75
 N = 1000  \(\sum\)fiui = 470

Mean number of heads per toss = A + \(\frac{\sum f_iu_i}{N}\)

\(=2+\frac{470}{1000}=2+0.47\)

\(=2.47\) 

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