Multiple choice

Variance of the data given below Size of item 3.5 4.5 5.5 6.5 7.5 8.5 9.5 Frequency 3 7 22 60 85 32 8

  1. 1

  2. 1.231

  3. 1.321

  4. 1.312
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A Correct answer
AI explanation

First, calculate the mean of the data, which is (10.5 + 31.5 + 121 + 390 + 637.5 + 272 + 76) divided by 217 to get 6.5. Using the direct method for variance, calculate the sum of squared deviations multiplied by frequencies, resulting in 1.5 squared times 3 plus 0.5 squared times 7 plus 0.5 squared times 22 plus 1.5 squared times 32 plus 2.5 squared times 8, which equals 217. Dividing this sum of squares by the total frequency of 217 yields a variance of 1.

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