The Range and Outliers

Averages are not the whole story

An average tells you a typical value, but it hides how spread out the data is. Two classes can both average 60% in a test, yet one might have everyone near 60 while the other has scores from 10 to 95. To capture that, we measure spread — and the simplest measure is the range.

Calculating the range

Range = highest value − lowest value

Worked example. Daily temperatures (°C): 12, 15, 9, 18, 11.

1. Highest value = 18.
2. Lowest value = 9.
3. Range = 18 − 9 = 9 °C.

The range is 9 °C. Notice the range is a single number describing spread — it is not a list, and it is not an average.

What the range tells you

A small range means values are close together — the data is consistent. A large range means values are spread out — the data is more varied.

Compare two players' bowling scores:

Player	Scores	Range
Amir	142, 138, 150, 145, 140	150 − 138 = 12
Beth	95, 180, 110, 165, 130	180 − 95 = 85

Both might average about 143, but Amir's range of 12 shows he is far more consistent, while Beth's range of 85 shows she is unpredictable. When you compare two data sets, quote both an average and the range — the average for the typical value, the range for the consistency.

What is an outlier?

An outlier is a value that sits far away from the rest of the data — much higher or much lower. Look at these house prices (in thousands): 210, 225, 218, 230, 980.

The value 980 is wildly different from the cluster around 220. It is an outlier, perhaps a luxury mansion among ordinary homes, or even a typing error.

How outliers distort the range

Because the range uses only the highest and lowest values, a single outlier at one end can blow it up.

• With the outlier: range = 980 − 210 = 770.
• Without the outlier: range = 230 − 210 = 20.

One unusual value changed the range from a tidy 20 to a misleading 770. The mean is affected too: the outlier drags it far above what most houses cost. The median, which is the middle value, barely moves — which is exactly why the median is often preferred when outliers are present.

Handling an outlier

When you meet an outlier, do not just delete it. Think:

1. Is it an error? A height of 1700 cm is impossible — likely 170 cm mistyped. Correct genuine mistakes.
2. Is it real but unusual? A genuine mansion belongs in the data, but you should report it and perhaps quote results both with and without it.
3. Choose robust measures. If outliers are present, the median and the interquartile range describe the data more fairly than the mean and the range.

Activity: hunt the outlier

1. Collect a small data set, such as the number of letters in each classmate's first name.
2. Add one deliberately strange value (imagine a name with 25 letters).
3. Calculate the range with and without it.
4. Calculate the mean with and without it.
5. Discuss which value is the outlier and how much it changed your results.

Why this matters

Spread is half the story of any data set, and ignoring outliers can lead to badly wrong conclusions in science, sport and finance. Pair this with the averages in mean, median, mode and range, and learn to read spread visually in bar charts and pictograms.