range() — Range (min to max)

range(x)

Key idea

• The range is the biggest value minus the smallest value — a simple measure of spread. (e.g. range of 4,9,15 = 15-4 = 11)
• It shows the full stretch from the smallest to the largest value.
• The range is very sensitive: one far-off value (an outlier) can stretch it a lot. (e.g. 4,9,150 -> range 146)
• It uses only two values, so it ignores everything in between.
• A range of 0 means all the values are the same. (e.g. 7,7,7 -> range 0)

Definition

$$\text{range}=\max (x)-\min (x)$$

$\max (x)$

the largest value

$\min (x)$

the smallest value

Where you'd use it

• Today’s hourly temperatures were 12, 15, 18, 22, 19 °C. range returns the low and high, 12 and 22, so the day spanned a 10 °C swing from coolest to warmest.
• A menu lists items at $4, $7, $12, $25. The range is $4 to $25, telling a diner at a glance the cheapest and priciest choices.
• Lap times in a race were 61, 59, 63, 58 seconds. range gives 58 and 63, the fastest and slowest laps, though one freak slow lap would widen this instantly.

Frequently asked questions

Does range() give one number?

No — it returns the min and max. Subtract them for the width.