Question

Consider a sample of numbers ranging from 3 to 120. The calculated mean of this sample is determined to be 132.4. Is this answer reasonable?

A) Yes, the mean can exceed the range of values in the sample.

B) No, the mean should always fall within the range of values in the sample.

C) Yes, the mean is a valid statistical measure that can be higher or lower than individual values in the sample.

D) No, the mean should be exactly within the midpoint of the range of values.

Answer 1

The mean of a sample ranging from 3 to 120 should always be within that range, so a calculated mean of 132.4 is not reasonable.

Step-by-step explanation:

When analyzing a sample of numbers ranging from 3 to 120, the mean (or arithmetic average) of the sample should reasonably fall within that range. If the calculated mean is 132.4, this is not a reasonable answer because the mean cannot exceed the maximum value in the sample, which in this case is 120. Therefore, the correct answer is B) No, the mean should always fall within the range of values in the sample. This is because the mean is calculated by summing all values and dividing by the number of values, which logically places the mean within the smallest and largest values.

Measures of central tendency, such as the mean, median, and mode, are powerful tools for summarizing data. The mean is particularly sensitive to outliers, or extreme values, which can skew the result. However, in a sample without such outliers, the mean will lie within the range of the sample values.