Finding a weighted mean from a table of counts

Every value here is exact and you are told how many times each one occurs. Nothing is approximated, so the answer is the true mean rather than an estimate.

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.

Birth weights

32 newborns, with the number of babies at each birth weight:

2 babies at 5 lb 7 at 6 lb 15 at 7 lb 8 at 8 lb

Find the mean birth weight. Round to at least one decimal place.

The transposed table

Same 32 newborns. Notice how ALEKS prints it: the count column comes first and the weight column second, the reverse of most tables you have seen.

A classmate multiplies down the first column and reports a mean of 8.0 pounds. What is the correct mean?

Divided by the wrong thing

A shop sold 48 coffees: 18 at $3, 22 at $4, 8 at $6.

Find the mean price paid. Round to two decimal places.

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

$\bar{x} = \dfrac{\sum f \cdot x}{\sum f}$ each value times how often it occurs

the total is the count, not the number of rows 32 babies, four rows

A weighted mean is the ordinary mean of a list you were spared writing out. Fifteen babies at 7 pounds is 7 written fifteen times; multiplying is just the shortcut. So the denominator is how many items there are in total, exactly as it would be if the list were written out in full.

Common slips

(1) Averaged the values and ignored the counts. That answers a question nobody asked. (2) Divided by the number of rows. Four rows, 32 babies; the 32 goes underneath. (3) Read the columns in the wrong order. ALEKS sometimes prints the count column first, which is the reverse of most tables.

04 Practice — Step by Step

Multiply, total, divide

A tutor recorded how many sessions each of her 25 students booked last term.

Sessions booked, 25 students
Number of students	Sessions booked
4	1
9	2
7	3
5	4

Find the mean number of sessions. Round to one decimal place.

Step 1

Read the table before you compute

Which column holds the values being averaged?

Step 2

The weighted total

What is $\sum f \cdot x$, the total number of sessions?

Step 3

The mean

Divide by the number of students. What is the mean?

Step 4

Estimate or exact?

Is 2.5 an estimate of the mean, or the actual mean?

Q6 Q8

Finding a weighted mean from a table of counts

The distinction that matters on this exam