Central tendency

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Concept #1.MEAN

The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discreteand continuous data, although its use is most often with continuous data. The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. So, if we have n values in a data set and they have values x₁, x₂, ..., x_n, then the sample mean, usually denoted by (pronounced x bar), is:

The mean includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

Learning objectives

1. Understand and know that a measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.
2. Understand that the mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of central tendency become more appropriate to use than others.
3. Learn to calculate mean and analyse data and make inferences.

Notes for teachers

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as, the median and the mode. The mean, median and mode are all valid measures of central tendency but, under different conditions, some measures of central tendency become more appropriate to use than others.

Activity

1. Activity No #1 central tendency mean activity1
2. Activity No #2 central tendency mean activity2

Concept #2.MEDIAN

Activity

1. Activity No #1 central tendency median activity1
2. Activity No #2 central tendency median activity2

Concept #3.MODE

Activity

1. Activity No #1 central tendency mode activity1
2. Activity No #2 central tendency mode activity2

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