How are measures of dispersion related to measures of central tendency?

Measures of dispersion, like standard deviation and interquartile range, give us information about how spread out the data is in a distribution. Measures of central tendency, like mean and median, give us information about where the center of the data is.

Mean and Standard Deviation

• The mean and standard deviation are often used together because they are based on all of the data values in a distribution. The mean tells us where the center of the data is, and the standard deviation tells us how spread out the data is around the mean. For example, if the mean height of students in a class is 5 feet tall with a standard deviation of 2 inches, we know that most students are within 2 inches of the mean height.

Median and Range

• The median and interquartile range are often used together because they are based on the middle 50% of the data values in a distribution. The median tells us where the center of the data is, and the interquartile range tells us how spread out the data is around the median. For example, if the median income of a group of people is $50,000 with an interquartile range of $20,000, we know that most people have an income within $20,000 of the median.
• The range, on the other hand, is not based on any measure of central tendency because it only looks at the minimum and maximum values in a distribution. The range tells us the distance between the smallest and largest values, but it doesn’t tell us where the center of the data is or how spread out the data is around the center.

In summary, measures of dispersion give us information about how spread out the data is, while measures of central tendency give us information about where the center of the data is. The mean and standard deviation are often used together, as are the median and interquartile range. The range does not correspond with any measure of central tendency.