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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

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 sumfx = 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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