Question

What proportion of the data points in a data set are expected to be within one standard deviation of the mean.

Answer 1

Approximately 68% of the data points in a data set are expected to be within one standard deviation of the mean because of the 68-95-99.7 rule.

Explanation:

This rule states that approximately 68% of the data points in a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Answer 2

Explanation:

Approximately 68% of the data points in a dataset are expected to be within one standard deviation of the mean, assuming that the data follows a normal distribution. This is known as the Empirical Rule or the 68-95-99.7 rule. According to this rule, approximately 95% of the data points are expected to be within two standard deviations of the mean, and approximately 99.7% of the data points are expected to be within three standard deviations of the mean.

Please note that this rule applies only to a normal distribution, if the data is not normally distributed, the proportion may be different.