22 A scientist measured the lengths of 240 gray seals from Muskeget Island and 120 gray seals from Sable Island. The scientist determined that the mean length of the 240 gray seals from Muskeget Island was 88 inches and the mean length of the 120 gray seals from Sable Island was 94 inches. What was the mean length of all 360 gray seals the scientist measured for this study?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The mean of a data set is calculated by dividing the sum of the values in the data set by the number of values in the data set. It’s given that 240 the mean length of the gray seals from Muskeget Island was 88 inches. This x =88 can be represented by the equation 240 , where x represents the sum of the 240 lengths, in inches, of the gray seals from Muskeget Island. Multiplying both 240 = 240 88 =21,120 sides of this equation by yields x ^ h^ h, or x inches. It’s also 120 94 given that the mean length of the gray seals from Sable Island was inches. y =94 This can be represented by the equation 120 , where y represents the sum of 120 the lengths, in inches, of the gray seals from Sable Island. Multiplying both 120 = 120 94 =11,280 sides of this equation by yields y ^ h^ h, or y inches. 360 Therefore, the sum of the lengths, in inches, of all gray seals is 21,120+11,280 32,400 360 32,400 90 , or . Dividing this sum by yields 360 , or inches. 360 Therefore, the mean length of all gray seals the scientist measured for this 90 study is inches. Choice A is incorrect and may result from conceptual or calculation errors. 94 Choice C is incorrect. This is the mean length of 88 inches and inches, not the 360 mean length of all gray seals the scientist measured for this study. Choice D is incorrect and may result from conceptual or calculation errors.
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