Relative Frequency
In short: Relative frequency is the count of one category divided by the total count, shown as a fraction, decimal or percent of the whole group.
8th GradeStatistics8.SP.A.4
What is Relative Frequency?
The relative frequency of a category compares its count with the total, which matters because 40 students choosing pizza is a lot in a class of 50 and almost nothing in a school of 2,000.
For a category with count \(f\) out of \(n\) observations, \(\text{relative frequency} = \frac{f}{n}\). All the relative frequencies in a table add up to 1, or 100% when written as percents.
How to spot it
- A question asks what fraction, share or percent of a group chose an option.
- You must compare two groups of different sizes fairly.
- A frequency table needs an extra column titled proportion or percent.
- A two-way table asks about the percent within one row or one column.
The method
- Find the count for the category you care about.
- Find the total number of observations in the group being studied.
- Divide the count by the total and simplify, or convert to a decimal.
- Multiply by 100 for a percent, and check that all categories sum to 100%.
Relative Frequency: solved example
Problem
A bakery sold 52 bagels, 41 muffins and 27 scones on Saturday. Find the relative frequency of each item as a percent, to the nearest tenth.
Solution
The total is \(52 + 41 + 27 = 120\).
Bagels: \(\frac{52}{120} \approx 43.3\%\). Muffins: \(\frac{41}{120} \approx 34.2\%\). Scones: \(\frac{27}{120} = 22.5\%\). The percents add to 100%, so 43.3%, 34.2% and 22.5%.
Try it
Question 1
9 of 36 students ride bikes to school. What is the relative frequency of biking?
Show the answer
\(\frac{9}{36} = \frac{1}{4} = 0.25\), or 25%.
Question 2
What do all the relative frequencies in a table add up to?
Show the answer
They add up to 1, which is 100%.
Relative Frequency vs. Frequency Table
The ordinary frequency is the raw count of a category, such as 18 dogs. The relative one scales that count by the total, 18 out of 40, so groups of different sizes can be compared. A table can show both columns side by side.
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Whole dictionary: A–Z · 8th Grade · Statistics