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 Mini-Lesson Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

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 v1

USH financial is examining the use of its midtown ATM machine. Here are the numbers of transactions made per day at this ATM during the past 9 days:

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

Find the range of the data set.

Daily temperatures v2

A weather station recorded the high temperature (in °F) on each of the last 8 days:

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

Find the range of the data set.

Package weights v3

A shipping clerk weighed 7 packages (in pounds):

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

Find the range of the data set.

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 How to Solve It

range = max − min

The simplest spread number: how wide is the gap between the largest and smallest values?

Find the maximum.

Data: 39, 46, 37, 9, 45, 10, 46, 39, 20.

max = 46 (appears twice, but only the value matters)

Find the minimum.

Scan the same list, looking for the smallest value:

min = 9

Easy to miss because 10 and 20 look small and appear earlier in the list. Sort or scan carefully.

Subtract.

range = 46 - 9 = 37

The number of transactions varies by up to 37 from day to day — a wide spread for ATM usage.

▸ COMMON SLIPS(1) Used 10 as the min. 9 is smaller than 10 and appears in the data set. Scan all values, not just the obvious ones. (2) Swapped max and min. Range is max − min and must be non-negative. If you get a negative number, you subtracted in the wrong order. (3) Reported max only (or min only). Range is the difference, not either endpoint.

04 Practice — Step by Step

Try one with decimals. Max minus min, same recipe.

Find the range.

7 package weights (lbs): 3.2, 5.8, 1.5, 7.4, 2.9, 4.6, 6.1. What is the range?

range =

▸ NICE WORK

You've walked through the whole problem.

That's the move. ALEKS will give you a different version with different numbers — but the steps are the same.

Q3 Q5