Data & Statistics — Core Skills

Data & Statistics: The Basics

Part 1 of 2 — Reading a Table and Turning It Into a Fraction

A two-way table sorts a group of people two ways at once. Here is one. It shows $50$ students, sorted by whether they are a boy or a girl, and by whether they answered Yes or No to a survey question.

	Yes	No	Total
Boys	12	8	20
Girls	18	12	30
Total	30	20	50

How to read it

Each box inside the table is called a cell, and it holds a count of people. The cell where the Girls row meets the Yes column holds $18$. That means $18$ girls answered Yes.

The Total column on the right adds across a row. The boys row: $12 + 8 = 20$, so there are $20$ boys.

The Total row along the bottom adds down a column. The Yes column: $12 + 18 = 30$, so $30$ students said Yes.

The bottom-right corner, $50$, is everyone in the table.

Turning a count into a fraction

A fraction is the part you want on top, and the whole group on the bottom.

What fraction of all $50$ students are girls who said Yes?

The part you want is the $18$ girls who said Yes. The whole group is all $50$ students. So the fraction is $\frac{18}{50}$.

Turning that fraction into a percent

A percent means "out of $100$." The quickest way here is to make the bottom number $100$.

$50 \times 2 = 100$, so multiply the top by $2$ as well: $18 \times 2 = 36$.

$\frac{18}{50} = \frac{36}{100} = 36\%$

If the bottom does not turn into $100$ easily, divide instead: $18 \div 50 = 0.36$, and moving the decimal point two places to the right gives $36\%$.

That is the whole skill: find the count, find the group it came from, put one over the other.

Data & Statistics: Practice

Part 2 of 2 — Count, Group, Fraction, Percent

Every one of these questions is the same four steps.

1. Find the count you want. This is one cell of the table, or one total. It goes on top of the fraction.
2. Find the group the question is asking about. "Of all $50$ students" means the group is everyone. "Of the boys" means the group is only the boys. This number goes on the bottom.
3. Write the fraction: $\frac{\text{count you want}}{\text{group}}$.
4. If the question asks for a percent, turn the fraction into a percent. Make the bottom number $100$ if you can, or divide the top by the bottom and move the decimal point two places to the right.

The words that tell you the bottom number

• "of all the students" or "of everyone surveyed" → use the grand total.
• "of the boys" or "among the boys" → use the boys total only.
• "of the students who said Yes" → use the Yes total only.

The top of the fraction is usually sitting right there in the table. The bottom is the part you have to think about, so read that phrase twice.

Totals reminder

A row total is the row added across. A column total is the column added down. If a question needs a total that is not printed, add the cells yourself.