From a sample of size 100, the following descriptive measures were calculated: m

Question

From a sample of size 100, the following descriptive measures were calculated: median = 23, mean = 20, standard deviation = 5, range = 35; seventy-five-sample values are between 10 and 30; and ninety-nine sample values are between 5 and 35. If you knew the sample mean, median, and standard deviation were correct, which one of the following conclusions might you draw?

A. The distribution is skewed to the right because the median exceeds the mean

B. The number of sample values between 10 and 30 was miscounted

C. The range must have been calculated incorrectly because it should not be seven times the standard deviation's value

D. The number of sample values between 5 and 35 must have been miscounted because all 100 values must be in this interval

Explanation / Answer

From a sample of size 100, the following descriptive measures were calculated: median = 23, mean = 20, standard deviation = 5, range = 35; seventy-five-sample values are between 10 and 30; and ninety-nine sample values are between 5 and 35. If you knew the sample mean, median, and standard deviation were correct, which one of the following conclusions might you draw?

A. The distribution is skewed to the right because the median exceeds the mean

B. The number of sample values between 10 and 30 was miscounted

C. The range must have been calculated incorrectly because it should not be seven times the standard deviation's value

D. The number of sample values between 5 and 35 must have been miscounted because all 100 values must be in this interval

we know that about 95% of the values are between (mean-2*sd, mean+2*sd) values.

mean-2*sd=20-2*10=10, mean+2*sd=20+2*10=30

There fore seventy-five-sample values are between 10 and 30 was miscounted.

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