Suppose you have a set of data which has a bell-shaped histogram.Compare the interquartile range with the range from one standard deviation below the mean to one standard deviation above the mean.The interquartile range is smaller.

Question

Quizplus · Accepted Answer

A bell-shaped histogram indicates a normal distribution. In a normal distribution, the interquartile range covers 50% of the data from the 25th percentile to the 75th percentile. One standard deviation below the mean to one standard deviation above the mean covers approximately the same proportion of data (68%). However, the interquartile range covers only the middle 50% of the data, while the range of one standard deviation below/above the mean includes the entire 68% of the data, making it larger than the interquartile range.

Suppose You Have a Set of Data Which Has a Bell-Shaped