Measures of central tendency: mean, median, mode

Central tendency tells us where the “centre” of a set of numbers lies. Think of it as the *average* spot that represents the whole group. We’ll explore three main measures: the mean, median and mode.

The mean is the sum of all values divided by the number of values. It’s like sharing a pizza equally among friends.

Formula: $\displaystyle \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$

Example: Ages of 5 students: 12, 14, 13, 15, 16. Sum = 12+14+13+15+16 = 70. Mean = $70 \div 5 = 14$.

Analogy: If you had 70 slices of pizza and 5 friends, each friend would get 14 slices on average.

The median is the middle value when the data are arranged in order. If there’s an even number of values, it’s the average of the two middle ones. It’s like finding the person standing in the middle of a line.

Example: Same ages: 12, 13, 14, 15, 16 (sorted). Median = 14 (the third value).

Analogy: If you line up people by height, the median is the one standing right in the middle of the line.

The mode is the value that appears most often. There can be one mode, no mode, or multiple modes (bimodal, trimodal, etc.). It’s like the most popular ice‑cream flavour at a party.

Example: Data: 2, 3, 3, 4, 5. Mode = 3 (appears twice).

Analogy: If you asked 10 friends their favourite colour and 4 said blue, blue is the mode.

1. Always check for outliers before calculating the mean.
2. When the data set is skewed, the median is usually a better measure.
3. Remember that a data set can have no mode (all values unique) or multiple modes.
4. For exam questions, state the measure you used and explain why it is appropriate.
5. Use the formula symbols correctly: $\bar{x}$ for mean, $x_{(k)}$ for median, and $m$ for mode.