IGCSE Maths / Working with data
Estimated mean and modal class for grouped data
Edexcel International GCSE Maths (4MA1), chapter 19: Working with data, specification point 6.2c-f. Free lesson.
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For grouped data, the original values are unknown, so you use class midpoints to estimate the mean. The modal class is the interval with the highest frequency.
Why the mean is only an estimate
A grouped table keeps the number of values in each class but not the individual values. To calculate a mean, you treat every value in a class as if it were at its midpoint. This gives a useful estimate, but it cannot give the exact mean because most values will not be exactly at the midpoint. Values above and below a midpoint tend to balance out, so the estimate can be close to the true mean.
How to estimate the mean
Find each class midpoint, then multiply it by that class's frequency. Add the frequency × midpoint values to estimate the total of all the data. Divide by the total frequency.
Worked example: puzzle times
Forty people were timed doing a puzzle. The grouped times and frequencies are shown below. Use each class midpoint as the estimated time for everyone in that class. 0 to 10 minutes: frequency 6 10 to 20 minutes: frequency 12 20 to 30 minutes: frequency 14 30 to 40 minutes: frequency 8
How to identify the modal class
The modal class is the interval with the highest frequency. Give the interval, not the frequency itself, because the question asks which group contains the most values. In the puzzle example, the highest frequency is 14, so the modal class is 20 to 30 minutes. The answer is an interval with two ends, not 14.
Finding a class's contribution
A class contributes its frequency multiplied by its midpoint to the estimated total. For a class from 20 to 40 with frequency 5, the midpoint is 30, so its contribution is 150.
More lessons in Working with data
- Bar charts, pie charts and pictograms
- Two-way tables and reading statistical diagrams
- Mean from a frequency table
- Frequency density
- Drawing a histogram
- Reading frequencies from a histogram
- Completing a histogram from a part drawn graph
- Estimating a frequency within a class
- Building a cumulative frequency table
- Plotting a cumulative frequency diagram
- Reading values from a cumulative frequency graph
- Estimating how many are above or below a value
- Estimating the median from a cumulative frequency diagram
- Estimating the interquartile range from a cumulative frequency diagram
- Comparing two cumulative frequency distributions
- Mean, median, mode and range
- Quartiles and the interquartile range for discrete data
- What a measure of spread tells you
- Using the interquartile range to compare distributions