The heights, x cm, of 200 boys and the heights, y cm, of 300 girls are summarized

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The heights, x cm, of 200 boys and the heights, y cm, of 300 girls are summarized by the following totals:

­Σ(x −160)2 = 18 240, Σ­(x −160) = 1820, Σ­(y −150)2 = 20 100, Σ­(y −150) = 2250.

a. Find the mean height of these 500 children.

b. By first evaluating ­x2 and ­y2, find the variance of the heights of the 500 children, including appropriate units with your answer.

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