Multiple choice

The SD and mean of a sample of 180 data are 6 and 110, respectively. Also, SD and the mean of another group of 220 data are 4 and 120, respectively. What is the value of combined variance of all the data?

  1. 12.44

  2. 36.44

  3. 49.75

  4. 56.75

  5. None of these
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C Correct answer
Explanation

The combined variance formula is used here. Given n1=180, mean1=110, var1=36 and n2=220, mean2=120, var2=16. The combined mean is (180*110 + 220*120)/400 = 115.5. Calculating the variance using the formula for combined groups yields 49.75.

AI explanation

Using the formula for combined variance, we first find the overall mean as ((180 multiplied by 110) plus (220 multiplied by 120)) divided by 400, which equals 115.5. We then apply the combined variance formula: (n1 times v1 plus n2 times v2 plus n1 times d1 squared plus n2 times d2 squared) divided by (n1 plus n2), where d1 and d2 are the differences between group means and the combined mean. Plugging in the numbers gives ((180 times 36) plus (220 times 16) plus (180 times 30.25) plus (220 times 20.25)) divided by 400, which calculates to 19900 divided by 400, resulting in a combined variance of 49.75.

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