Mean, median and mode from a frequency table
A survey counts the members in each family of a tole. Add more families of five to the frequency table, and watch how the mean, the median and the mode each change, or stay put.
Core concept
For discrete data in a frequency table, the mean is Σfx ÷ N, the median is the ((N + 1)/2)th value and the mode is the value with the biggest frequency; new data move the mean every time, but the median and the mode only when enough values change
Topic: Measures of central tendency
A survey of a tole counted the members in each family: 3 families of 2, 6 of 3, 8 of 4, some of 5 (f5) and 2 of 6. In a frequency table, x is the value (members) and f is how many times it comes (the number of families). The number of families is N = Σf. The mean is Σfx ÷ N: multiply each value by its frequency, add, and divide. The median is the middle family when all are put in order: the ((N + 1)/2)th value, found with cumulative frequency. The mode is the value with the biggest frequency. Grouped data, such as heights in class intervals, use the same ideas with classes in place of single values: see the lab on heights in our class.
What you will learn
- Find N = Σf and Σfx from a frequency table.
- Calculate the mean of discrete data as Σfx ÷ N.
- Find the median with cumulative frequency, and the mode.
- Explain why the mean, median and mode react differently to new data.
Before you start
- Know how to find the mean of a list of numbers.
Materials
- A notebook to make the frequency table
Equipment
- A calculator
Procedure
- Record the table with no families of 5 (f5 = 0).
- Make f5 = 6 and record.
- Make f5 = 10 and record.
- Make f5 = 16 and record.
How this simulation is simplified
- The other frequencies stay 3, 6, 8 and 2; f5 is even, so N is odd and the median is one family.