Averages from frequency tables, and estimating the mean of grouped data with midpoints.
What you will learn
- Work out the mean, median and mode from a frequency table
- Estimate the mean of grouped data using midpoints
- Find the modal class and the class that contains the median
A frequency table is a list in short form
A row "2 pets, frequency 7" means the value 2 appears 7 times.
To find the mean, multiply each value by its frequency, add these up, then divide by the total frequency.
| Number of pets | Frequency | Pets × frequency |
|---|---|---|
| 0 | 5 | 0 |
| 1 | 8 | 8 |
| 2 | 4 | 8 |
| 3 | 3 | 9 |
| Total | 20 | 25 |
Mean = 25 ÷ 20 = 1.25 pets. The mode is the value with the highest frequency (1 pet). The median is the middle of all 20 values: the 10th and 11th are both 1, so the median is 1.
To find which value is in a position, use running totals of the frequencies: 5, 13, 17, 20. The 10th and 11th values come after the first 5 (the zeros) and within the first 13, so they are 1s.
In general the median is the (n + 1) ÷ 2 th value: for 20 values that is the 10.5th, halfway between the 10th and 11th.
The total of all the values is the total of the last column (25 pets here), and the total frequency (20) is how many there are. "At least 2 pets" means 2 or more: 4 + 3 = 7 people.
With a missing frequency x, write the mean as an equation. If the frequencies are 3, x and 2 for the values 1, 2 and 3, and the mean is 1.9, then the total is 3 + 2x + 6 = 9 + 2x and the total frequency is 5 + x.
So (9 + 2x) ÷ (5 + x) = 1.9, which gives 9 + 2x = 9.5 + 1.9x, so 0.1x = 0.5 and x = 5. Notice x appears in both the total and the total frequency.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- A frequency table is a list in short form
- Grouped data: use the midpoints
- Divide by the right number
- Try it: First question
8 practice questions, marked as you go; about 25 minutes in all.
Key terms
Total frequency, Estimate, Modal class
In this unit: Statistics and charts
Averages and range, frequency tables, charts and diagrams, scatter graphs and sampling, and (Higher) cumulative frequency, box plots and histograms.