Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
In a group of 20 people, 8 prefer football. In another group of 50 people, 15 prefer it. Which group likes football more? Comparing 8 and 15 is useless: the groups are not the same size! We need a measure that takes the total into account: that is the frequency.
The frequency of a category is the share it represents of the total: frequency = count divided by total count. For the first group: 8 ÷ 20 = 0.4. We can write it as a percentage: 0.4 = 40%. For the second: 15 ÷ 50 = 0.3 = 30%. Now we can compare: 40% versus 30%, the first group is the bigger football fan.
A frequency is always between 0 and 1 (or between 0% and 100%). And if you add up the frequencies of all the categories, you always get 1, that is 100%: everyone is counted somewhere.
Frequencies can also be read on charts. On a pie chart, the size of each sector shows the frequency directly: half the disc means 50%; a quarter of the disc means 25%.
In this lesson you will compute frequencies, switch between decimal form and percentages, and go the other way too: find a count from a frequency. It is a key tool for reading the world: polls, elections, sports statistics.
In a group of 20 people, 8 prefer football. What is the frequency of this choice, in decimal form then as a percentage?
8 ÷ 20 = 0,4
I divide the count (8) by the total count (20): the frequency is 0.4.
0,4 = 40/100 = 40 %
To get a percentage, I multiply by 100: 0.4 is 40 out of 100, so 40%.
Result: The frequency is 0.4, that is 40%.