Math

Mean, Median, and Mode

2 min readEasy5-question drill

Almost every SAT statistics question starts with mean, median, or mode — and the test loves to make you work backwards from an average to find a missing value. Master these three and you unlock a whole cluster of easy points.

Where this lesson fits

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→One-Variable Data: Distributions and Measures of Center and Spread →Percentages

These three words are all ways to describe the "center" of a list of numbers. They sound similar, but they mean different things — and mixing them up is the #1 way students lose points here.

Mean is the plain old average. Add up all the numbers, then divide by how many numbers there are.

mean = (sum of all values) ÷ (number of values)

For example, the mean of 4, 6, 8 is (4 + 6 + 8) ÷ 3 = 18 ÷ 3 = 6.

Here's the trick the test loves: rearrange that formula to get the sum:

sum = mean × (number of values)

Whenever a problem says "the mean of 8 numbers is 12.5," your first move should be to find the total: 12.5 × 8 = 100. The sum is the hidden bridge in almost every hard mean problem.

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The three measures of center

Measure	How to find it	Example: 4, 4, 6, 10
Mean	Add all, divide by count	(4+4+6+10)/4 = 6
Median	Middle of sorted list	(4+6)/2 = 5
Mode	Most frequent value	4

Same data set, three different 'centers.'

Median is the middle value when the numbers are lined up in order from smallest to largest. Two rules:

If there's an odd number of values, the median is the single middle one.
If there's an even number of values, the median is the average of the two middle values.

So for 3, 5, 9 the median is 5. For 3, 5, 9, 11 the median is (5 + 9) ÷ 2 = 7. You must put the numbers in order first — this is the most common slip-up.

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Seven ages in order — the median is the 4th value, 9, sitting in the middle.

Mode is the value that appears most often. In 72, 85, 85, 90, 98, the mode is 85 because it shows up twice and everything else shows up once. A list can have no mode (all values appear equally) or more than one mode.

A quick way to keep them straight:

Mean = add and divide (average).
Median = middle (think "medi-an" = "median" of a road).
Mode = most frequent (both start with "mo").

One more thing the test checks: outliers (extreme values) pull the mean but barely touch the median. If a billionaire walks into a room, the average income skyrockets, but the median hardly moves.

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Quick check

The ages of 7 children in a class are 6, 8, 8, 9, 10, 11, 12. What is the median age?

9.5

Worked examples

Example 1

The test scores for five students are 72, 85, 85, 90, 98. What is the mode of the scores?

Example 2

The ages of 7 children are 6, 8, 8, 9, 10, 11, 12. What is the median age?

Example 3

The mean of 8 numbers is 12.5. If one number, 16, is removed, what is the mean of the remaining 7 numbers?

Common pitfalls

Forgetting to order the list before finding the median

The median is the middle of the sorted list. If you grab the middle of an unsorted list, you'll get the wrong number. Always rewrite the values in order first.

Confusing mean with median or mode

The test deliberately puts the mean as a wrong answer choice when asking for mode (or vice versa). Re-read which one the question wants before choosing.

Mishandling an even-count median

With an even number of values, there is no single middle — you must average the two middle numbers. Picking just one of them is a common error.

Solving for individual numbers instead of the sum

On 'missing value' problems, you almost never need each number. Convert the mean to a total with sum = mean × count, then work with the total.

Key takeaways

Mean = add all values and divide by how many there are; remember sum = mean × count.
Median = the middle value of the ordered list (average the two middle values if the count is even).
Mode = the value that appears most often; a list can have none or several.
Outliers shift the mean a lot but barely move the median.
On missing-value mean problems, find the total first, adjust it, then divide by the new count.

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Try it yourself

5 practice questions on Mean, Median, and Mode, drawn from the question bank. The tutor is one click away if you get stuck.

Where this lesson fits

Mean, Median, and Mode

You are here

→One-Variable Data: Distributions and Measures of Center and Spread →Percentages