Cumulative frequency · Grade 10
In Grade 10 you learn: cumulative frequency graphs.
Cumulative frequency is a running total of the frequencies in grouped data. Plot each total at the upper end of its class and join the points with a smooth curve; then read off the median, the quartiles and how many values lie above or below any value.
Key facts
- Cumulative frequency is the running total of the frequencies.
- Plot each cumulative frequency at the upper end of its class and join the points.
- Median ≈ the value at n/2 on the cumulative frequency axis. Q1 is at n/4 and Q3 at (3n)/4.
- Interquartile range = Q3 − Q1: the spread of the middle half of the data.
- Estimated mean of grouped data = Σ(f × midpoint) ÷ Σf.
Worked examples
Example 1
The times 40 people spent in a shop were grouped: 0–10 min: 4, 10–20: 10, 20–30: 14, 30–40: 8, 40–50: 4. Estimate the median time.
Answer: About 24.3 minutes
Example 2
Estimate the mean time for the shop data in the first example.
Answer: About 24.5 minutes
Example 3
A cumulative frequency graph shows 80 values. Where do you read the median?
Answer: At a cumulative frequency of 40
Example 4
40 people were timed. The cumulative frequency at 30 minutes is 26. How many people took longer than 30 minutes?
Answer: 14