H3.3

Name two measures of the center of a​ distribution, and state the conditions under which each is preferred for describing the typical value of a single data set. What are two measures of the center of a​ distribution?

Mean and median are both designed as different ways to find what is a​ "typical" value of the distribution.

Name two measures of the variation of a​ distribution, and state the conditions under which each measure is preferred for measuring the variability of a single data set.

The interquartile range is preferred when the data is strongly skewed or has outliers. The standard deviation is preferred when the data is relatively symmetric.

The interquartile range tells us how much space the​ _____ of the data occupy.

The interquartile range tells us how much space the middle​ 50% of the data occupy. It is found by subtracting the third quartile from the first quartile.

When a distribution is​ skewed, the​ _______ is used to measure the center and the​ _______ is used to measure variation.

The mean and standard deviation are used to measure the center and​ variation, respectively, when a distribution is symmetric.

Under what conditions is the mean​ preferred?

The mean provides a good measure of center when the data is relatively symmetric.

For what purpose is the median​ used?

The median is a typical value of a data set. It is used particularly when the distribution is skewed.

The median is often used for which of the following types of​ distribution?

The median is often used for skewed distributions. The mean is not often used for skewed distributions because skew affects the mean more than it affects the median.

The value that would be right in the middle if you were to sort the data from smallest to largest is called the​ ______.

The median is the value that would be right in the middle if you were to sort the data from smallest to largest. About​ 50% of the observations are below it and about​ 50% of the observations are above it.

Under what conditions is the median​ preferred?

The median provides a better measure of center when the data is skewed or has outliers because the presence of an outlier has a much greater effect on the mean.