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Find the variance of 10, 12, 23, 23, 16, 23, 21, 16

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Answer
24\boxed{24}

Checking the result, the sum of the squared deviations from the mean is 192192, and dividing by 88 gives a population variance of 2424.

Problem: Find the variance of the dataset: 10,12,23,23,16,23,21,1610, 12, 23, 23, 16, 23, 21, 16.

Steps

  1. Find the mean
    μ=10+12+23+23+16+23+21+168=1448=18\mu = \frac{10 + 12 + 23 + 23 + 16 + 23 + 21 + 16}{8} = \frac{144}{8} = 18
  2. Subtract the mean and square each deviation
    (10−18)2+(12−18)2+(23−18)2+(23−18)2+(16−18)2+(23−18)2+(21−18)2+(16−18)2(10-18)^2 + (12-18)^2 + (23-18)^2 + (23-18)^2 + (16-18)^2 + (23-18)^2 + (21-18)^2 + (16-18)^2
    =(−8)2+(−6)2+52+52+(−2)2+52+32+(−2)2= (-8)^2 + (-6)^2 + 5^2 + 5^2 + (-2)^2 + 5^2 + 3^2 + (-2)^2
    =64+36+25+25+4+25+9+4=192= 64 + 36 + 25 + 25 + 4 + 25 + 9 + 4 = 192
  3. Divide by the number of data points (population variance)
    σ2=1928=24\sigma^2 = \frac{192}{8} = 24

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