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Miscellaneous Exercise 8 (II) · Q40
Q.

Following data gives no. of goals scored by a team in 100 matches. Compute the standard deviation.

No. of Goals Scored012345
No. of matches5202515205
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Step 1: Sum the printed frequencies: 5+20+25+15+20+5=905+20+25+15+20+5=90. This does not match the stated '100 matches' in the question — the frequency table itself totals 90, not 100. Being transparent about this mismatch, the computation below uses the actual printed frequencies (total 90).

Step 2: N=90N=90. ∑fixi=0(5)+1(20)+2(25)+3(15)+4(20)+5(5)=220\sum f_ix_i = 0(5)+1(20)+2(25)+3(15)+4(20)+5(5)=220, so xˉ=220/90≈2.44\bar{x}=220/90\approx2.44.

Step 3: ∑fixi2=0+20+100+135+320+125=700\sum f_ix_i^2 = 0+20+100+135+320+125=700. …

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