Descriptive Statistics

Descriptive statistics condense large datasets into simple summaries. They help you understand the shape, centre, and spread of your data before moving on to more complex analyses.

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Measures of Central Tendency

Central tendency describes where the "middle" of a dataset lies.

Mean (Arithmetic Average)

The mean is the sum of all values divided by the number of values:

x̄ = (x₁ + x₂ + ... + xₙ) / n

Example: For the data set {4, 8, 6, 5, 3, 7, 9}

x̄ = (4 + 8 + 6 + 5 + 3 + 7 + 9) / 7 = 42 / 7 = 6

Note: The mean is sensitive to outliers. A single extreme value can pull the mean far from the typical value.

Median

The median is the middle value when data is sorted in ascending order.

• If n is odd, the median is the centre value.
• If n is even, the median is the average of the two centre values.

Example: Sorted data {3, 4, 5, 6, 7, 8, 9} → Median = 6

Mode