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SSAT MIDDLE LEVEL • QUANTITATIVE

Compute and compare averages from data.

Averages summarize data sets, like finding the typical score in your favorite game.

SECTION 1

The Story Behind Averages

People have used averages for thousands of years. Long ago, Babylonians calculated them for astronomy. In the 1800s, scientists like Francis Galton made averages popular in everyday life. Today, you see averages in sports scores and test grades. They help make sense of lots of numbers fast.

2000 BCE
Babylonians use averages to predict planet paths, like tracking a soccer ball's average speed.
1662
Early Statistics
John Graunt studies London deaths to find average lifespans.
1880s
Modern Term
Francis Galton coins 'average' for typical values in nature.
Today
Computers calculate averages instantly for games and apps.

Averages solve the problem of too much data. Imagine 20 test scores. Which one shows how the class did? Averages give you that quick picture.

SECTION 2

Core Types of Averages

There are three main averages: mean (add up and divide), median (middle value), and mode (most common). Each works best in different situations. Mean uses every number. Median ignores extremes. Mode shows favorites.

1

Mean

Total sum divided by count. Great for even data.
2

Median

Middle number in ordered list. Best against outliers.
3

Mode

Most frequent value. Perfect for categories.
⚽ Quick Analogy
Think of averages like game stats. Mean is total points divided by games, like your season average. Median skips one bad game. Mode is your go-to move that scores most.
SECTION 3

Seeing Averages on a Number Line

Data points plotted on a number line. The mean pulls toward the outlier at 9. Median and mode stay at 5.

This diagram shows how averages differ. The big 9 pulls the mean right. Median splits the middle. Mode repeats twice. You can see why we compare them! Great job spotting the patterns.

SECTION 4

Formulas for Averages

Each average has a simple formula. Start with the data list. Order it for median. Count repeats for mode. You can do these without a calculator.

MEAN
mean = (x₁ + x₂ + … + xₙ) ÷ n
x₁ to xₙ are data values. n is the count. Like (2+3+5+5+9) ÷ 5 = 4.8.
MEDIAN
middle value (ordered list)
Odd count: middle one. Even: average of two middles. Order: 2,3,5,5,9 → 5.
MODE
most frequent value
5 appears twice. No mode or bimodal if tie.
SECTION 5

Comparing in Different Data Sets

Histograms compare symmetric (bell shape) and skewed data. In symmetric, all averages match. Skewed outlier changes mean but not median.

Skewed data tilts like a lopsided stack of blocks. Mean slides toward the heavy side. Median stays center. You're getting good at this!

SECTION 6

Step-by-Step Calculation

Quiz scores: 70, 85, 85, 90, 60. Find all three averages. Order first: 60, 70, 85, 85, 90. Easy steps ahead. You can do it!

Basketball Free Throws Example
1
Step 1 — MeanSum: 60 + 70 + 85 + 85 + 90 = 390. Divide by 5: 390 ÷ 5 = 78
78
2
Step 2 — MedianOrdered list middle: third value = 85
85
3
Step 3 — Mode85 appears twice: most frequent = 85
85
💡 Tip
Low 60 pulls mean down. Median and mode show stronger performance. Compare wisely!
SECTION 7

When to Use Each Average

Choose based on your data!
AverageStrengthLimit
MeanUses all data.Outliers change it.
MedianIgnores extremes.Ignores most data.
ModeShows most common.May not exist.
✦ KEY TAKEAWAY
Like picking a bat in baseball: mean for total power, median for steady hits, mode for your favorite swing. Match to the game!
SECTION 8

Beyond Basic Averages

Basic averages lead to cool tools like range or quartiles. Range is max minus min. It shows spread. SSAT might ask to compare with averages.

BasicAdvanced
Mean, median, modeRange, quartiles, weighted mean
Center onlyCenter + spread

These build your skills for harder problems. Practice now, shine later!

SECTION 9

Test Your Skills

PROBLEM 1 — CONCEPTUAL
What does the median represent? (A) Most frequent (B) Middle value (C) Total sum (D) Biggest number (E) Average difference
PROBLEM 2 — BASIC CALCULATION
Find the mean of 4, 6, 8. (A) 4 (B) 6 (C) 8 (D) 18 (E) 5
PROBLEM 3 — INTERMEDIATE
Scores: 10, 20, 20, 30, 40. Median? (A) 20 (B) 25 (C) 30 (D) 24 (E) 20 and 30
PROBLEM 4 — APPLIED
Game scores: 5,6,7,8,50. Mean=15.2, median=7. Best for typical score? (A) Mean (B) Median (C) Both (D) Neither (E) Mode
PROBLEM 5 — CRITICAL THINKING
House prices: $100k, $110k, $120k, $130k, $1M. Which average for 'typical' home? (A) Mean (B) Median (C) Mode (D) Range (E) Min

Awesome work! Review weak spots and try again. You're SSAT ready.

SUMMARY

Key Points to Remember

Master mean (sum ÷ count), median (middle), and mode (most common). Compare for best fit—outliers hurt mean most.

Visuals like number lines show why. Practice builds speed. You've got this for the SSAT!

Varsity Tutors • SSAT Middle Level • Compute and compare averages from data.