Averages and range

Adjust real data, frequency tables and box plots to see how the mean, median, mode, range and IQR are actually calculated.

Curriculum rangeYears 6-11

Adjust any value with + / − and watch every average update live.

Sorted: 3, 4, 7, 7, 7, 9, 12

\text{Mean} = \dfrac{\text{sum of values}}{\text{how many values}} = \dfrac{4 + 7 + 7 + 9 + 12 + 3 + 7}{7} = 7

\text{Median (middle value)} = 7

Mode = 7

\text{Range} = \text{highest} - \text{lowest} = 12 - 3 = 9

Learning notes

Averages and range essentials

Keep these rules beside you while you explore and practise.

Mean uses every value; median is the middle value when sorted; mode is the most common value; range measures spread, not an average.

\text{Mean} = \dfrac{\sum x}{n}

\text{Mean} = \dfrac{\sum fx}{\sum f}

For grouped data this is only an estimate, since you use the midpoint of each class, not the real values.

Minimum, lower quartile (Q1), median, upper quartile (Q3), maximum. A box plot draws all five in one diagram.

\text{IQR} = Q3 - Q1

💡A data set can have no mode, one mode, or several modes -- but it always has exactly one mean, median and range.