http://www.ck12.org Chapter 6. Measures of Central Tendency - Basic
6.1 The Mean
Learning Objectives
- Understand the mean of a set of numerical data.
- Compute the mean of a given set of data.
- Understand the mean of a set of data as it applies to real world situations.
Introduction
You are getting ready to begin a unit in Math that deals with measurement. Your teacher wants you to use benchmarks
to measure the length of some objects in your classroom. A benchmark is simply a standard by which something can
be measured. One of the benchmarks that you can all use is your hand span. Every student in the class must spread
their hand out as far as possible and places it on top of a ruler or measuring tape. The distance from the tip of your
thumb to the tip of your pinky is your hand span. Your teacher will record all of the measurements. The following
results were recorded by a class of thirty-five students:
TABLE6.1:
Hand span (inches) Frequency
612 1
714 3
712 8
734 10
814 7
812 4
914 2Later in this lesson, we will compute the mean or average hand span for the class.
The term “central tendency” refers to the middle value or a typical value of the set of data which is most commonly
measured by using the three m’s –mean, median and mode. In this lesson we will explore the mean and then move
onto the median and the mode in the following lessons.
The mean, often called the ’average’ of a numerical set of data, is simply the sum of the data numbers divided by the
number of numbers. This value is referred to as an arithmetic mean. The mean is the balance point of a distribution.
Example 1:In a recent hockey tournament, the number of goals scored by your school team during the eight games
of the tournament were 4,5,7,2,1,3,6,4. What is the mean of the goals scored by your team?
Solution:You are really trying to find out how many goals the team scored each game.
- The first step is to add the number of goals scored during the tournament.
4 + 5 + 7 + 2 + 1 + 3 + 6 + 4 = 32 (The sum of the goals is 32)- The second step is to divide the sum by the number of games played.