Central Tendency
Calculating mean, median, mode, range, standard deviation, and quartiles — numeric summary statistics
Generate Unlimited Practice Questions
Sign up for free and get 50 practice questions to start your prep.
Start Free PracticeLearn 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 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! 📊
Practice Questions
5 practice questions for SSAT Middle Level
What is the mean of the list of numbers above?
Show Solution
- To find the mean, add all the numbers together and divide by the total number of values in the list. The sum is . Since there are 6 numbers, the mean is .
Show Solution
- If the mean of four tests is 85, the sum of all four test scores must be . The sum of the first three tests is . To find the fourth test score, subtract the sum of the first three tests from the total sum: .
If is the median for the list of seven numbers above, what is the least possible value of ?
Show Solution
- The median is the middle number of the ordered list. The six known numbers in increasing order are 12, 17, 28, 35, 41, and 50. For to be the exact middle (the 4th number out of 7), it must be greater than or equal to 28 and less than or equal to 35, which means . Therefore, the least possible value of is 28.
Show Solution
- The original total weight of the 4 cats was pounds. The total weight increased by pounds. The new total weight of the cats is pounds. The new mean weight is pounds.
Show Solution
- The mode is the number that appears most frequently in a list. In this list, the number 45 appears twice, and the number 52 appears three times. All other numbers appear only once. Since 52 appears the most, it is the mode.
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 (). 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 !
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.