Median, Mode and Range Made Simple

S6Median, Mode and Range

Middle, most common, spread.

Median = middle of the ordered list; mode = most common; range = spread.

Scores: 3, 5, 3, 9, 7.

Ordered: 3, 3, 5, 7, 9

Median
5
middle value

Mode
3
appears twice

Range
6
9 − 3

ORDER FIRST — median and range only work on a sorted list.

Learn the 3 Measures

1Median: order, then middle.

Sort the list, cross off from both ends to the centre. 3, 3, 5, 7, 9 → median 5.

middle = 5

2Mode: the most common.

The value that appears most often. 3 appears twice → mode 3. (No repeats → no mode.)

mode = 3

3Range: biggest − smallest.

9 − 3 = 6. The range measures spread, not an average.

9 − 3 = 6

💡 Key IdeaEven count? The median is halfway between the middle two: for 2, 4, 6, 10 it's (4 + 6) ÷ 2 = 5.

Worked Example

Find the median, mode and range of 12, 8, 12, 15, 8, 12.

Order

8, 8, 12, 12, 12, 15

→

Median (even count)

middle two: 12 and 12 → 12

→

✓ All three

median 12 · mode 12
range 15 − 8 = 7

Watch Out! Common Mistakes

Skipping the ordering step.

3, 5, 3, 9, 7 → median 3 ✕

Order first! Sorted: 3, 3, 5, 7, 9 → the middle is 5.

Mode = biggest number.

mode of 3,3,5,7,9 = 9 ✕

Wrong! Mode = MOST COMMON, not largest: 3.

Range as ‘from x to y’.

range = “3 to 9” ✕

One number! Range = biggest − smallest = 9 − 3 = 6.

⬇ Cheat Sheet

MEDIAN, MODE AND RANGE

ORDER the list first, always.
Median = middle value (even count → mean of middle two).
Mode = most common value.
Range = biggest − smallest (a single number).

Example: 3,5,3,9,7 → sorted 3,3,5,7,9 → median 5, mode 3, range 6.

📖 Continue Your Journey

✓ S1 Tally Charts and Pictograms ✓ S2 Bar Charts ✓ S3 Line Graphs ✓ S4 Pie Charts ✓ S5 The Mean S6 Median, Mode and Range S7 Two-Way Tables S8 Venn and Carroll Diagrams S9 Probability Basics S10 Statistics Problem Solving

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Next Lesson: S7 Two-Way TablesRows and columns that cross-check.

📄 Free printable: Download the Median, Mode and Range cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Always order the list first.
Median: the middle value; with an even count, halfway between the middle two.
Mode: the most common value — there can be one, several or none.
Range: biggest minus smallest — a measure of spread, given as one number.

Frequently asked questions

What is the difference between mean, median and mode?

The mean shares the total equally (total ÷ count); the median is the middle of the ordered list; the mode is the most common value. They can all be different for the same data.

How do you find the median of an even number of values?

Take the two middle values of the ordered list and find the number halfway between them: for 2, 4, 6, 10 the median is (4 + 6) ÷ 2 = 5.

What is the range?

Biggest value minus smallest value — it measures how spread out the data is, and it's written as a single number.