http://www.ck12.org Chapter 5. Measures of Central Tendency
The termcentral tendencyrefers to the middle, or typical, value of a set of data, which is most commonly measured
by using the 3 m’s−mean, median and mode. The mean, median, and mode are known as themeasures of central
tendency. In this concept, we will explore the mean, and then we will move on to the median and the mode in the
following concepts.
Themean, often called theaverageof a numerical set of data, is simply the sum of the data values divided by the
number of values. This is also referred to as the arithmetic mean. The mean is the balance point of a distribution.
To calculate the actual mean of your handfuls of blocks, you can use the numbers that were posted on your grid paper.
These posted numbers represent the number of blocks that were picked by each student in your class. Therefore,
you are calculating the mean of a population, which is a collection of all elements whose characteristics are being
studied. You are not calculating the mean number of some of the blocks, but you are calculating the mean number
of all of the blocks. We will use the example below for our calculations:
From the grid paper, you can see that there were 30 students who posted their numbers of blocks. The total number
of blocks picked by all the students can be calculated as follows:
1 × 2 + 2 × 3 + 3 × 4 + 5 × 5 + 3 × 6 + 4 × 7 + 3 × 8 + 2 × 9 + 3 × 10 + 3 × 11 + 1 × 12
2 + 6 + 12 + 25 + 18 + 28 + 24 + 18 + 30 + 33 + 12 = 208
The sum of all the blocks is 208, and the mean is the number you get when you divide the sum by the number of
students who placed a post-it-note on the grid paper. The mean number of blocks is, therefore,^20830 ≈ 6 .93. This
means that, on average, each student picked 7 blocks from the pail.
When calculations are done in mathematics, formulas are often used to represent the steps that are being applied.
The symbol∑means “the sum of“ and is used to represent the addition of numbers. The numbers in every question
are different, so the variablexis used to represent the numbers. To make sure that all the numbers are included, a
subscript is often used to name the numbers. Therefore, the first number in the example can be represented asx 1.
The number of data values for a population is written asN. The mean of the population is denoted by the symbolμ,
which is pronounced "mu." The following formula represents the steps that are involved in calculating the mean of
6.2 Variance of a Data Set
Mean=sum of the values
the number of valuesThis formula can also be written using symbols: