Understanding Mean and Variability

This lesson covers comparing groups using measures of center and variability, including mean and median. Activities involve comparing heights of sports teams and analyzing family heights. The lesson explains mean absolute deviation and includes optional activities on song lengths. Homework and review conclude the session.

What is a measure of center in statistics?

• A value that represents the middle of a data set

• A way to determine the frequency of data points

• A method to calculate the range of data

• A technique to find the highest value in a data set

Which of the following is NOT a measure of variability?

• Range

• Median

• Mean Absolute Deviation

• Interquartile Range

In the comparison of gymnastics and volleyball teams, what was the main observation?

• Volleyball team has a greater range of heights

• Both teams have the same average height

• There is no overlap in heights between the two teams

• Gymnastics team is taller than the volleyball team

How is the mean calculated for a data set?

• By counting the frequency of each value

• By subtracting the smallest value from the largest

• By adding all values and dividing by the number of values

• By finding the middle value

What does the median represent in a data set?

• The most frequently occurring value

• The average of all values

• The difference between the highest and lowest values

• The middle value when data is ordered

What effect does adding two 18-inch tall individuals have on Jada's family mean height?

• It increases the mean height

• It decreases the mean height

• It has no effect on the mean height

• It doubles the mean height

What is the purpose of calculating the mean absolute deviation (MAD)?

• To find the average distance of each data point from the mean

• To determine the highest value in a data set

• To calculate the total sum of all data points

• To identify the most frequent data point

Which data set has a mean absolute deviation of 0.30?

• Data set C

• Data set B

• Data set A

• Data set D

What does a higher mean absolute deviation indicate about a data set?

• The data points are closer to the mean

• The data points are more spread out from the mean

• The data set has fewer data points

• The data set has more frequent values

If a data set has a mean of 8 and a MAD of 1.2, how does it compare to other data sets with lower means?

• It has longer data points

• It has shorter data points

• It has the same data point length

• It has more frequent data points