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  3. For which of the following bird species is the standard deviation of the numbers of sightings shown for the four seasons least?

For which of the following bird species is the standard deviation of the numbers of sightings shown for the four seasons least?

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问题 For which of the following bird species is the standard deviation of the numbers of sightings shown for the four seasons least?
选项 A、Cardinal
B、Junco
C、Robin
D、Sparrow
E、Wren
答案D
解析 Recall that the standard deviation of the numbers in a list is a measure of the spread of the numbers about the mean of the numbers. The standard deviation is directly related to the differences \x - m\ between the mean m and each number x in the list. The smaller the differences, the smaller the standard deviation. Thus to answer the question, look at the values of \x — m\ for each of the five bird species in the answer choices and determine which species has the smallest values.
Choice A, Cardinal. For cardinals, the numbers of sightings are 30, 18,11, and 20. The mean is approximately 20. Therefore the differences between the mean and the four numbers in the list are approximately 10, 2, 9, and 0.
Choice B, Junco. For juncos, the numbers of sightings are 12, 0, 0, and 6. The mean is approximately 5. Therefore the differences between the mean and the four numbers in the list are approximately 7, 5, 5, and 1.
Choice C, Robin. For robins, the numbers of sightings are 6, 12, 28, and 18. The mean is 16, and the differences between the mean and the four numbers in the list are 10, 4, 12, and 2.
Choice D, Sparrow. For sparrows, the numbers of sightings are 20, 19, 23, and 22. The mean is 21, and the differences between the mean and the four numbers in the list are 1, 2, 2, and 1.
Choice E, Wren. For wrens, the numbers of sightings are 0, 18, 30, and 12. The mean is 15, and the differences between the mean and the four numbers in the list are 15, 3, 15, and 3.
Consider how consistently small the differences are for the numbers of sightings of sparrows as compared to the differences for the other four species. From this you can judge that the numbers of sightings of sparrows has the least standard deviation. Thus the correct answer is Choice D.
This explanation uses the following strategies.
Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation
Strategy 9: Estimate
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