Finding a mean from tabular data

Two questions, one method: multiply each value by how many times it occurs, add, and divide by the count. The second version uses class midpoints because the exact values are gone.

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 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.

From a frequency distribution

Daily drug dosages for 33 patients:

0 to 49: 5 · 50 to 99: 12 · 100 to 149: 10 · 150 to 199: 4 · 200 to 249: 2

Using class midpoints, estimate the mean dosage. Round to one decimal place; use four or more decimals in intermediate steps.

A midpoint

A frequency distribution has the class 150 to 199.

What midpoint represents that class?

Weighted, small numbers

A class of 20 students scored: 4 scored 6, 9 scored 8, 7 scored 10.

What is the mean score? 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

$\bar{x} = \dfrac{\sum (\text{value} \times \text{frequency})}{\sum \text{frequency}}$ the denominator counts observations, not rows

grouped data → use the class midpoint as the value midpoint = (lower + upper) ÷ 2

A weighted mean is the ordinary mean with the repeats collapsed. Instead of writing 2,300 seven times and adding, you multiply once. The denominator is still the number of observations — 37 computers, not 4 price rows.

Common slips

(1) Divided by the number of rows. Four price bands does not mean divide by 4. (2) Averaged the values, ignoring frequency. That is the unweighted mean and it is a different number. (3) Used a class bound instead of the midpoint. For 50 to 99 the representative value is 74.5, not 50 or 99.

04 Practice — Step by Step

Multiply, add, divide

Thirty-seven customers reported what they paid for a computer:

7 paid $2,300 · 10 paid $800 · 15 paid $2,700 · 5 paid $1,300

Find the mean price, to the nearest dollar.

Step 1

The weighted total

Multiply each price by its count and add: 7(2300) + 10(800) + 15(2700) + 5(1300).

Step 2

The count

How many computers is that?

Step 3

The mean

71,100 ÷ 37, to the nearest dollar.

Q15 Q17

Finding a mean from tabular data

Why weighting matters