Range of a data set

Maximum minus minimum. The simplest measure of spread — sensitive to outliers but quick to compute. Watch your eyes: the minimum is easy to miss in an unsorted list.

01 Worked Example Video

Every step of Range of a data set explained on video. Pause anywhere; the embed scrolls independently of the page.

YOUTUBE

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

ATM transactions

Transactions per day at an ATM for 9 days:

39, 46, 37, 9, 45, 10, 46, 39, 20

Find the range of the data set.

range =

Daily temperatures

High temperature (°F) for 8 days:

72, 68, 81, 55, 79, 64, 70, 73

Find the range of the data set.

range =

Package weights

Weights of 7 packages (lb):

3.2, 5.8, 1.5, 7.4, 2.9, 4.6, 6.1

Find the range.

range =

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

range = max − min the simplest measure of spread

Watch your eyes on the min smallest values are easy to miss in an unsorted list

Range measures how wide the data is: biggest value minus smallest. It’s fast to compute but sensitive to outliers — one extreme value pulls the range way out. See it live: [14, 8, 22, 5, 17, 11, 9] in the Center & Spread Visualizer → then flip on the outlier toggle to feel how the range explodes when one value drifts far.

Common slips

(1) Missed a small value in an unsorted list. The min might be tucked in the middle. Sort mentally or scan carefully. (2) Reported max and min separately. Range is the difference — subtract. (3) Used mean or median. Range isn’t a measure of center; it’s a measure of spread.

04 Practice — Step by Step

Practice this problem step by step

Data: 14, 8, 22, 5, 17, 11, 9. Find the range.

Step 1

What is range?

The range of a data set is:

Step 2

Find the max

In [14, 8, 22, 5, 17, 11, 9], what’s the largest value?

max =

Step 3

Compute the range

The min is 5 (tucked in the middle of the unsorted list). Compute 22 − 5.

range =

Q3 Q5

Range of a data set

You walked the range calculation end to end.