Statistics & Data Interpretation — Core Skills

Statistics & Data Interpretation: The Basics

Part 1 of 2 — Mean, Median, and Range

A list of numbers is called a data set. The SAT asks three questions about a list over and over. Each one has a short, fixed recipe. Learn the three recipes and you can answer these questions every time.

The three words

• Mean — the average. Add up all the numbers, then divide by how many numbers there are.
• Median — the middle number after you put the list in order from smallest to largest.
• Range — the biggest number minus the smallest number. It tells you how spread out the list is.

Mean and median both describe the center of a list. Range describes the spread.

Worked example

Use this list: $4, 8, 6, 10, 2$

Mean. Add every number:

$4 + 8 = 12$

$12 + 6 = 18$

$18 + 10 = 28$

$28 + 2 = 30$

There are $5$ numbers, so divide by $5$: $30 \div 5 = 6$. The mean is $6$.

Median. Put the list in order first. This step is not optional, and skipping it is the most common mistake on these questions:

$2, 4, 6, 8, 10$

Now find the middle. There are $5$ numbers, so the middle one is the third: $6$. The median is $6$.

Range. The biggest number is $10$ and the smallest is $2$. Subtract: $10 - 2 = 8$. The range is $8$.

One extra case: an even-length list

If the list has an even number of values, there are two middle numbers. Add those two and divide by $2$.

For $4, 6, 8, 10$, the two middle numbers are $6$ and $8$. So the median is $\frac{6 + 8}{2} = \frac{14}{2} = 7$.

That is everything. Add and divide for mean, put in order and look at the middle for median, subtract for range.

Statistics & Data Interpretation: Practice

Part 2 of 2 — Run the Recipes

Here are the three recipes in order. Read the question first and decide which word it is asking for: mean, median, or range.

1. Mean (the average). Add every number in the list. Then divide that total by how many numbers are in the list.
2. Median (the middle). Put the list in order from smallest to largest. If the count is odd, the median is the number in the middle. If the count is even, add the two middle numbers and divide by $2$.
3. Range (the spread). Find the biggest number and the smallest number. Subtract: biggest minus smallest.

Two habits that save points

• For the median, write the sorted list down. Do not try to sort it in your head.
• For the mean, count how many numbers are in the list before you divide. Circle them if it helps.

What spread means

A bigger range means the numbers are more spread out. A smaller range means they are packed close together.

For example, $8, 9, 10$ has a range of $10 - 8 = 2$, so those numbers sit close together. But $2, 9, 16$ has a range of $16 - 2 = 14$, so those numbers are much more spread out — even though both lists have the same middle value.