Resources | Subject Notes | Mathematics
This section covers the three main measures of central tendency: mean, median, and mode. These are used to describe the 'typical' value in a dataset.
The mean is the average of a set of numbers. To calculate the mean, you add up all the values in the dataset and then divide by the total number of values.
Formula:
$ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} $
Example: Consider the dataset: 2, 4, 6, 8, 10
Sum of values = 2 + 4 + 6 + 8 + 10 = 30
Number of values = 5
Mean = $\frac{30}{5} = 6$
The median is the middle value in a dataset that is ordered from least to greatest. If there is an even number of values, the median is the average of the two middle values.
Steps to find the median:
Example 1 (Odd number of values): Consider the dataset: 1, 3, 5, 7, 9
The median is 5 (the middle value).
Example 2 (Even number of values): Consider the dataset: 1, 3, 5, 7
The two middle values are 3 and 5.
Median = $\frac{3 + 5}{2} = 4$
The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all.
Example 1 (Unimodal): Consider the dataset: 2, 4, 4, 6, 8
The mode is 4 (it appears twice).
Example 2 (Bimodal): Consider the dataset: 2, 2, 4, 4, 6, 8
The modes are 2 and 4 (they both appear twice).
Example 3 (No mode): Consider the dataset: 1, 2, 3, 4, 5
No value appears more than once, so there is no mode.
| Measure | Formula | Description |
|---|---|---|
| Mean | $ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} $ | The average of the dataset. |
| Median | Find the middle value in an ordered dataset. | The middle value when the dataset is ordered. |
| Mode | The value that appears most often. | The most frequent value in the dataset. |
Understanding these measures of central tendency is crucial for interpreting and summarizing data in statistics.