0580
Averages and Range
Statistics
Using the frequencies
- A frequency table lists each value alongside how many times it occurs, so the frequencies must be used as counts
- Read the mode as the value against the biggest frequency, not that frequency figure itself
- The mean needs the total of all the data, found by multiplying each value by its frequency and adding
- Mean = Σ(frequency × value) ÷ total frequency
- The median is found by counting through the frequencies until the middle position is reached
- With n values the median sits at position (n + 1) ÷ 2
- Adding an extra column for frequency × value keeps the working visible and is what the method marks reward
Exam tip
The mode is the value with the biggest frequency, never the frequency itself, and the median is found by counting up the frequency column rather than reading the middle row. "The mean" is asked in 21 of the 43 papers; for a frequency table it is the total of frequency × value divided by the total frequency, not the mean of the value column.
Worked example
Averaging when values repeat
The table records the number of goals scored in 20 matches: 0 goals in 5 matches, 1 goal in 8, 2 goals in 4 and 3 goals in 3. Find the mean number of goals.
Solution:
- Multiply each number of goals by its frequency
- 0 × 5 = 0, 1 × 8 = 8, 2 × 4 = 8, 3 × 3 = 9
- Total goals = 0 + 8 + 8 + 9 = 25
- Total matches = 5 + 8 + 4 + 3 = 20
- Mean = 25 ÷ 20 = 1.25 goals
- The answer is not a whole number, which is perfectly acceptable for a mean