In this post, we’ll explore the three fundamental measures of descriptive statistics: Mean, Median, and Mode. These are essential tools for summarizing data and identifying key patterns. To illustrate, we’ll use the following dataset:
1, 9, 3, 7, 4, 6, 3
Mean: The Average
The mean (or arithmetic average) is calculated by summing all values and dividing by the number of values.
Formula:
Mean = (Sum of all values) / (Number of values)
Example Calculation:
Mean = (1 + 9 + 3 + 7 + 4 + 6 + 3) / 7 = 33 / 7 ≈ 4.71
The mean is useful for data that is symmetrically distributed and not affected by extreme outliers.
Median: The Middle Value
The median represents the middle value of a sorted dataset.
- If the number of values is odd: The median is the middle value.
- If the number of values is even: The median is the average of the two middle values.
Odd number example:
Sorted dataset: 1, 3, 3, 4, 6, 7, 9
Middle value: 4
Even number example:
Sorted dataset: 1, 3, 3, 4, 5, 6, 7, 9
Middle value: (4 + 5) / 2 = 4,5
The median is particularly useful when dealing with skewed distributions or datasets with outliers, as it is less affected by extreme values than the mean.
Mode: The Most Frequent Value
The mode is the number that appears most frequently in a dataset.
Example Calculation:
Dataset: 1, 9, 3, 7, 4, 6, 3
The number 3 appears twice, while all other numbers appear only once.
Mode = 3
A dataset can have:
- No mode (if all values are unique)
- One mode (unimodal, like in our example)
- Multiple modes (bimodal, multimodal)
The mode is particularly useful when analyzing categorical data or finding the most common value in a dataset.