Averages from Frequency Tables
Averages from frequency tables means finding the mode, median, mean and range of data that has already been grouped into a frequency table, rather than listed as individual values. This GCSE Statistics topic requires using running totals, or midpoints for grouped continuous data, to estimate these summary statistics accurately.
Method
- For the mode, read off the value (or class) with the highest frequency directly from the table.
- For the median, use the frequencies to find a running total (cumulative frequency) and locate the middle value's position.
- For the mean, multiply each value by its frequency, add these products up to get the sum, then divide by the total frequency.
- For grouped data (class intervals), use the midpoint of each class instead of an exact value, since the exact values inside a class are not known.
- Present the mean to the accuracy asked for, and remember it is only an estimate when using grouped data.
- To find a missing frequency from a given mean, set up an equation using sum(f x x) divided by sum(f), then solve for the unknown.
Worked example
The frequency table shows the number of siblings of 25 pupils: 0 siblings, frequency 5; 1 sibling, frequency 9; 2 siblings, frequency 7; 3 siblings, frequency 4. Calculate the mean number of siblings per pupil.
- Multiply each value by its frequency: 0 x 5 = 0, 1 x 9 = 9, 2 x 7 = 14, 3 x 4 = 12.
- Add these products: 0 + 9 + 14 + 12 = 35.
- Add the frequencies: 5 + 9 + 7 + 4 = 25.
- Divide the total by the number of pupils: 35 / 25.
- Final answer: mean = 1.4 siblings.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A survey of 24 pupils recorded the number of books read last month: 0 books frequency 5, 1 book frequency 8, 2 books frequency 7, 3 books frequency 4. Calculate the mean number of books read, correct to 2 decimal places.
A weather station recorded the number of rainy days in each of 20 weeks: 0 days frequency 3, 1 day frequency 6, 2 days frequency 5, 3 days frequency 4, 4 days frequency 2. (a) Write down the mode. (b) Find the median number of rainy days.
A group of students recorded the time, t minutes, spent on homework one evening: 0 <= t < 10 frequency 4, 10 <= t < 20 frequency p, 20 <= t < 30 frequency 6, 30 <= t < 40 frequency 2. The estimated mean time was 18 minutes. One frequency value, p, is unknown. Find the value of p.
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