每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

The mean height of the students in Juan's math class is equal to the mean height of the students in his English class. However, while the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches. Which of the following statements must be true?

A.The mean height of the students in Juan's English class is 2.9 inches greater than the mean height of the students in his math class.
B.The median height of the students in Juan's English class is 2.9 inches greater than the median height of the students in his math class.
C.The median height of the students in Juan's math class is 2.9 inches greater than the median height of the students in his English class.
D.The heights of the students in Juan's math class are less variable than the heights of the students in his English class.

答案和解析

答案：D

解析：

Choice D is correct. In a data set, standard deviation measures the amount of dispersion (variation) from the mean (average). A low standard deviation indicates that the data points tend to be close to the mean (low variability) and a high standard deviation indicates that the data points are more spread out relative to the mean (high variability).

Because the standard deviation of the heights of the students in Juan's math class (3.2 inches) is less than the standard deviation of the heights of the students in his English class (6.1 inches), it can be determined that the heights of the students in his math class have less variability than the heights of the students in his English class.