# Mean

### Mean

In this section, we practice calculating the mean of a data set. You may think your math teacher is mean if she says you are average! The word mean is often used simultaneously with the word average. The mean is calculated by dividing the sum of a set of values by the number of values in the set. In this section, we use the mean of a data set to make predictions about the data. In this section, we are first given sets of data and asked to calculate the mean of each set. Then, we are given word problems and asked to make predictions about given sets of data, using what we know about the mean. For example, we are asked to determine how a given set of data would need to change in order to alter the mean by a specified amount.

#### Lessons

• Introduction
a)
What is mean absolute deviation (MAD)?

• 1.
Calculate the mean of each set of data. Round your answer to the nearest tenth.
a)
4, 8, 9, 7, 7

b)
4.5, 5, 5.1, 10, 13.4, 2, 1

c)
81, 50, 82, 99, 213, 75

• 2.
A survey collected information about the total amount of time teens spent on computers each week. Only data from four cities is listed below.
 Cities Computer time (hours per week) A 15.3 B 17.5 C 12.4 D 13.9
a)
What is the mean for the four cities listed? Round your answer to the nearest tenth.

b)
If the mean for all cities in the country was 16.2 hours, would you predict the mean of the cities not listed to be more or less than 16.2 hours?

• 3.
Harry was given the following marks on his English essays:
69%, 71%, 85%, 80%, 93%, 99%
a)
Calculate his mean mark? Round your answer to the nearest whole percent.

b)
What mark would he need to receive on the next essay to increase his mean by 2 percent for the seven essays?

c)
Harry's friend, Thomas, received the following marks on his English essays:
96%, 74%, 75%, 66%, 96%, 90%
What is Thomas's mean mark? Round your answer to the nearest whole percent.

d)
Who has a smaller mean absolute deviation? Harry or Thomas? What does this tell you?