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Computing & Comparing
Averages

Master the mean to summarize data, solve word problems, and compare groups on the SSAT.

SSAT Middle Level

What Is an Average?

An average (also called the mean) is a single number that represents the "center" of a group of values. It tells you what each value would be if every item in the set were exactly equal.

Visualizing the Mean

3 7 5 9 6 Avg = 6

Why Do Averages Matter?

Summarize Data
One number can represent an entire set of scores, prices, or measurements.
Compare Groups
Averages let you compare two teams, classes, or time periods at a glance.
Predict & Plan
Knowing an average helps estimate future outcomes and set goals.

The Mean Formula

$$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$

Two Key Relationships

Find the Sum
If you know the mean and the count:
\( \text{Sum} = \text{Mean} \times n \)
Find a Missing Value
Compute the required sum from the target mean, then subtract the known values.

Mean vs. Median vs. Mode

Mean Median Mode
Definition \( \text{Sum} \div \text{count} \) Middle value Most frequent value
Uses all values? Yes Only position Only frequency
Sensitive to outliers? Yes No No
SSAT frequency Very common Common Occasional

How to Compute an Average

1
List all values. Write them out so nothing is missed.
2
Add them up. Compute the total sum carefully.
3
Count the values. Make sure you include every item: \( n \).
4
Divide. Compute \( \text{Sum} \div n \) to get the mean.
5
Check. Verify the mean is between the smallest and largest value.

Example 1: Basic Average

Find the average of 12, 18, 7, 23, 10.

STEP 1: SUM
\( 12 + 18 + 7 + 23 + 10 = \) 70
STEP 2: COUNT
\( n = \) 5 values
STEP 3: DIVIDE
\( \text{Mean} = \frac{70}{5} = \) 14

Example 2: Find a Missing Value

Sara scored 85, 92, and 78 on three tests. What must she score on the fourth test to have an average of 88?

1
Target sum: \( 88 \times 4 = \) 352
2
Current sum: \( 85 + 92 + 78 = \) 255
3
Missing score: \( 352 - 255 = \) 97

Example 3: Comparing Two Groups

Team A scored 14, 18, 22. Team B scored 20, 16, 19, 17. Which team has the higher average?

Team A 14 18 22 Avg=18 Team B 20 16 19 17 Avg=18

Combining Groups: Weighted Average

When two groups have different sizes, you cannot just average the two means. You must account for how many values are in each group.

How a New Value Shifts the Mean

Add a value above the mean
The average increases.
Add a value below the mean
The average decreases.
Add a value equal to the mean
The average stays the same.

Common Mistakes to Avoid

✕ Wrong Count
Forgetting to include a value (or counting one twice) changes your \( n \) and ruins the result.
✕ Averaging Averages
You cannot simply average two group means if the groups have different sizes. Use the weighted formula.
✕ Confusing Mean & Median
"Average" on the SSAT means the mean. The median is a different calculation: sort, then find the middle.

Quick Reference Table

Task Formula Example
Find the mean \( \frac{\text{Sum}}{n} \) \( \frac{30}{5} = 6 \)
Find the sum \( \text{Mean} \times n \) \( 6 \times 5 = 30 \)
Find missing value \( \text{Target sum} - \text{Known sum} \) \( 40 - 30 = 10 \)
Weighted mean \( \frac{n_1 \cdot \bar{x}_1 + n_2 \cdot \bar{x}_2}{n_1 + n_2} \) \( \frac{3(80)+7(90)}{10} = 87 \)

Question 1 of 5

What is the average of 15, 20, 25, 30, and 10?

Question 2 of 5

The average of four numbers is 12. What is their sum?

Question 3 of 5

Maria's test scores are 90, 85, and 92. What score does she need on a fourth test to have an average of 90?

Question 4 of 5

Class A has 5 students with an average score of 80. Class B has 15 students with an average score of 90. What is the combined average of all 20 students?

Question 5 of 5

The average of a set of 6 numbers is 15. If one number is removed and the new average becomes 14, what number was removed?