Introduction to expectation

A survey of a few hundred, a campus of a few thousand. Turn the sample into a rate, then apply that rate to everyone.

01 Worked Example 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 Recognize the Question

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

Straight scale-up

In a sample of 150 shoppers, 42 said they use the self-checkout. The store serves 1,800 shoppers a day.

How many would you expect to use the self-checkout? Round to the nearest whole number.

Different rate

Of 250 commuters surveyed, 105 said they would use a new rail link. The corridor serves 1,500 commuters.

How many would you expect to use it? Round to the nearest whole number.

Spot the slip

Of 180 students surveyed, 63 ride the bus. The campus has 2,400 students. A student answered 63.

What is the correct expected number?

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

rate = (count in the sample) ÷ (sample size) step one

expected = rate × population step two

The word expected here means the number you would predict if the whole population behaved like the sample. It is a projection, not a guarantee, and it need not come out whole — which is why these questions tell you how to round.

Common slips

(1) Answering the sample count. The survey number is an input, not the answer. (2) Dividing by the population instead of multiplying. The expected count must be bigger than the sample count when the population is bigger. (3) Rounding the rate before scaling. These questions say not to round intermediates, and on large populations an early round moves the answer by whole people.

04 Practice — Step by Step

Rate first, then scale

The transport office surveyed a random sample of students about how they get to campus. Here are the results.

Mode	Number of students
Bus	63
Car	47
Bicycle	38
Walk	32

There are 2,400 students in total.

Based on this information, how many students would we expect to travel by bus? Round to the nearest whole number. Do not round any intermediate calculations.

Step 1

The sample size

How many students were surveyed altogether?

Step 2

The rate

63 bus riders out of 180. As a decimal.

Step 3

Multiply or divide by 2,400?

You have a rate of 0.35 and a population of 2,400.

Step 4

The expected count

0.35 × 2,400.

Q10 Q12

Introduction to expectation

63 in the sample, 840 on campus