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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 - CBSE Class 10 - Mathematics

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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

Solution 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

Solution 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

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Solution 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 Concept: Mean of Grouped Data.
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