SSAT Upper Level

Central Tendency

Calculating mean, median, mode, range, standard deviation, and quartiles — numeric summary statistics

Generate Unlimited Practice Questions

Learn This Topic

Imagine you and your friends just played a massive tournament of your favorite video game. Some of you scored super high, and some... well, let's just say they are still learning! 🎮 How do you figure out who the "typical" player is? That's where Central Tendency comes in! It is just a fancy math term for finding the middle or typical score in a group of numbers.

On the SSAT, you will become a Data Detective 🕵️‍♂️. You will use three main tools to solve number mysteries: the Mean, the Median, and the Mode.

The Mean is the "fair share" average. If you brought 12 slices of pizza 🍕 and shared them equally among 4 friends, everyone gets $\frac{12}{4} = 3$ slices.

The Median is the monkey in the middle! If you line up everyone's heights from shortest to tallest, the median is the person standing exactly in the center.

The Mode is the most popular number. It's the score that shows up the most often, like the most popular shoe color in your classroom!

Finally, the test might ask you for the Range. This isn't a "middle" number, but it tells us how spread out the numbers are. You just take the biggest number and subtract the smallest number.

The SSAT loves to test what happens when you change the data. For example, what happens to the average if you add a super high score? (It goes up!) What happens to the range if everyone gets 5 bonus points? (It stays exactly the same!) Keep your detective hat on, and these questions will be a breeze! 📊

Key Formula

Mean = \frac{Total Sum}{Number of Items}

(And its secret backwards version:

Total Sum = Mean \cdot Number of Items

)

Practice Questions

5 practice questions for SSAT Upper Level

Q1 Hard

The mean of five numbers is 18. If four of the numbers are 12, 15, 20, and 24, what is the fifth number?

A 17

B 18

C 19

D 20

E 21

Show Solution

The sum of the five numbers is $5 \times 18 = 90$ . The sum of the four given numbers is $12 + 15 + 20 + 24 = 71$ . The fifth number must be $90 - 71 = 19$ .

Answer: C

Q2 Hard

The mean weight of five boxes is 14 pounds. The weights of three of the boxes are 10 pounds, 12 pounds, and 15 pounds. What is the mean weight, in pounds, of the remaining two boxes?

A 15.5

B 16

C 16.5

D 17

E 33

Show Solution

The total weight of all five boxes is $5 \times 14 = 70$ pounds. The sum of the weights of the three known boxes is $10 + 12 + 15 = 37$ pounds. The total weight of the remaining two boxes is $70 - 37 = 33$ pounds. Their mean weight is $\frac{33}{2} = 16.5$ pounds.

Answer: C

Q3 Hard

The scores of seven students on a math quiz are 88, 74, 95, 82, 78, 91, and 85. What is the median score?

A 82

B 84

C 85

D 88

E 91

Show Solution

To find the median, first order the scores from least to greatest: 74, 78, 82, 85, 88, 91, 95. Since there are seven scores, the median is the middle value, which is the fourth score in the ordered list: 85.

Answer: C

Q4 Hard

The numbers in a set are 5, 8, 8, 11, and 15. If a sixth integer,

x

, is added to the set, the mean of the new set will be equal to its median. Which of the following could be the value of

x

A 1

B 4

C 8

D 10

E 13

Show Solution

The sum of the original five numbers is $5 + 8 + 8 + 11 + 15 = 47$ . When $x$ is added, the new mean is $\frac{47 + x}{6}$ . Let's test the choices. If $x = 1$ (Choice A), the set becomes {1, 5, 8, 8, 11, 15}. The median is the average of the two middle numbers: $\frac{8 + 8}{2} = 8$ . The mean is $\frac{47 + 1}{6} = \frac{48}{6} = 8$ . Since the mean equals the median, 1 is the correct value.

Answer: A

Q5 Hard

Maria has an average (mean) score of 84 on her first four science tests. What score must she earn on her fifth test to raise her average to 86?

A 86

B 88

C 90

D 92

E 94

Show Solution

Maria's total score for the first four tests is $4 \times 84 = 336$ . To have an average of 86 after five tests, her total score must be $5 \times 86 = 430$ . The score she needs on the fifth test is the difference between these totals: $430 - 336 = 94$ .

Answer: E

Tips & Strategies

Always put your numbers in order from smallest to biggest before finding the median! If you just pick the middle number from a scrambled list, it's a trap! 🪤
Use the 'Total Sum' trick! If a question tells you 'the average of 4 numbers is 10', immediately multiply them to find the total sum ( $4 \cdot 10 = 40$ ). This is the secret key to unlocking almost every SSAT average problem! 🗝️

Common Mistakes

Watch out for confusing the words! Mean, Median, and Mode all start with 'M'. Remember: Mean is mean (you have to do the most math), Median has a 'd' for middle, and Mode starts with 'Mo' for Most!
Don't forget that Range is a subtraction problem. Some students just write down the biggest number they see. Always do $Highest - Lowest$ !

Frequently Asked Questions

What if there are two middle numbers when I look for the median?

Great question! If you have an even number of items, there is no single middle number. Just take the two numbers in the center, add them together, and divide by 2 (you are finding their mean)!

Can a set of numbers have more than one mode?

Yes! If two numbers tie for being the most popular, you can have two modes (we call this 'bimodal'). If no number repeats at all, there is no mode!

Will I have a calculator on the SSAT to find the mean?

Nope! The SSAT does not allow calculators. The good news is that the test makers usually pick friendly numbers that divide nicely, so practice your basic division skills!

What happens to the mean if I add a number that is exactly the same as the current mean?

It stays exactly the same! If your average test score is 90, and you get a 90 on your next test, your overall average is still 90.

Generate Unlimited Practice Questions

Learn This Topic

Practice Questions

Tips & Strategies

Common Mistakes

Frequently Asked Questions

Related Topics

More Data, Statistics & Probability

Other Levels

Browse

Generate Unlimited Practice Questions