Choosing Appropriate Statistical Measures

Which describes how to find the MEAN?

• add all of the values and then divide by the number of values

• sort the data and find the middle value

Which describes how to find the MEDIAN?

• add all of the values and then divide by the number of values

• sort the data and find the middle value

Which are good descriptors of this distribution?

• symmetric

• bell-shaped

• uniform

• skewed left

• skewed right

Answer explanation

This distribution is symmetric because there is a clear center and the left side is a mirror image of the right. It is also bell-shaped because most of the data is clustered near the center.

Which are good descriptors of this distribution?

• symmetric

• bell-shaped

• uniform

• skewed left

• skewed right

Answer explanation

This distribution is skewed left because there are two extreme values on the left side of the distribution.

Which statement is true for this distribution?

• The mean is greater than the median

• The mean equals the median

• The mean is less than the median

Answer explanation

Because distribution is perfectly symmetric, the mean will be equal to the median.

Which statement is true for this distribution?

• The mean is greater than the median

• The mean equals the median

• The mean is less than the median

Answer explanation

Because distribution is skewed left, the mean will include low values, causing it to be low. The low values do not affect the median because there is a large peak at the center.

Which statistical measure is most appropriate for measuring the center of this data?

• mean

• median

Answer explanation

Because distribution is symmetric and not skewed, we use the mean, which gives equal weight to all values in the data set.

Which statistical measure is most appropriate for measuring the center of this data?

• mean

• median

Answer explanation

Because this distribution is skewed left, the mean will be distorted by extreme values. Therefore, the median is the more appropriate measure of center.

Which statistical measure is most appropriate for measuring the variability of this data?

• standard deviation

• interquartile range

Answer explanation

The distribution is symmetric and not skewed, so we usually use the standard deviation to measure variability, because it gives equal weight to all values in the data set.

Which statistical measure is most appropriate for measuring the variability of this data?

• standard deviation

• interquartile range

Answer explanation

Because this distribution is skewed left, the standard deviation will be distorted by extreme values. Therefore, the interquartile range is the more appropriate measure of variability.