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Measures of Central Tendency
Concept sheet | Mathematics
Secondary
3
Table of contents
A measure of central tendency describes the statistical value around which the data in a distribution is concentrated.
In other words, measures of central tendency are a way of summarizing a set of data into a single value. Here are the 3 most commonly used measures of central tendency.
Mean, Median, Mode
Moments in the video:
- 00:27-Mode
- 00:43-Median
- 01:03-Mean
- 01:26-Example
- 02:28-- CORRECTION There is a "2" missing in the calculation.
- 03:28-Conclusion
Mean, Median, Mode: Frequency Table
Moments in the video:
- 00:27-Finding the mode
- 00:45-Calculating the median
- 03:05-Calculating the mean
- 04:37-Conclusion
Mean, Median, Mode: Grouped Data
Moments in the video:
- 00:30-Finding the modal class
- 00:47-Calculating the medial class
- 02:19-Calculating the mean
- 04:06-Conclusion
The Mean
The mean is the centre of equilibrium of a distribution. In general, the mean is the value that each data item in the distribution would have if the total data was equally divided among them.
A secondary school principal analyzes the grades of 2 different secondary 2 classes. Instead of looking at the results one by one, he decides to analyze the average grade of each class.
This way, the principal can compare the classes as if all the students in a class had gotten the same grade.
The Mode
The mode is the most frequently occurring data value in the studied distribution.
A car manufacturer wants to create a sensation by proposing a new colour for a certain model of vehicle. To help him make his choice, he carries out a survey on a sample of 100 people and compiles the data in the following table.
|
Colour |
Lime Green |
Fire Orange |
Grape Purple |
Azure Blue |
Wishful Grey |
|---|---|---|---|---|---|
|
Number of respondents |
12 |
15 |
25 |
43 |
5 |
The most popular (trendy) colour is azure blue. To increase his chances of satisfying his future customers, he chose this new colour and will make it available for a vehicle model.
The Median
The median is the centre value that separates a group into 2 equal parts. The median is very useful in box-and-whisker plots (quartile diagrams).
In a hiring process for a federal public service job, the goal is to retain the best candidates, in terms of their results in |\%.| Here are the scores obtained:
|62,| |64,| |65,| |65,| |66,| |68,| |69,| |72,| |75,| |\boldsymbol{\color{#ec0000}{79}},| |80,| |81,| |82,| |82,| |84,| |85,| |86,| |87,| |89|
To significantly reduce the size of the group, half of the applications are eliminated. To establish the minimum selection score, the median is used, which is |79.|