GB-32-05-001 · Cumulative frequency
The table shows waiting times t in minutes.
| Time | Frequency |
|---|---|
| 0 < t ≤ 10 | 4 |
| 10 < t ≤ 20 | 15 |
| 20 < t ≤ 30 | 18 |
| 30 < t ≤ 40 | 22 |
(a) Write the cumulative frequencies at 10, 20, 30 and 40 minutes.
(b) On squared paper, draw a cumulative frequency graph.
Part (a)
Cumulative Frequency: Drawing
Booklet p. 69
Method
1) Add a cumulative-frequency column
2) Plot upper class boundaries, starting at the lower boundary with frequency zero
3) Join with a smooth increasing curve
Worked Example (GB-32-05-001 · Part (a))
Write the cumulative frequencies at 10, 20, 30 and 40 minutes.
1)
| Time | Frequency | Cumulative frequency |
|---|---|---|
| 0 < t ≤ 10 | 4 | 4 |
| 10 < t ≤ 20 | 15 | 19 |
| 20 < t ≤ 30 | 18 | 37 |
| 30 < t ≤ 40 | 22 | 59 |
Ans =
4, 19, 37, 59
Part (b)
Cumulative Frequency: Drawing
Booklet p. 69
Method
1) Add a cumulative-frequency column
2) Plot upper class boundaries, starting at the lower boundary with frequency zero
3) Join with a smooth increasing curve
Worked Example (GB-32-05-001 · Part (b))
On squared paper, draw a cumulative frequency graph.
1)
| Time | Frequency | Cumulative frequency |
|---|---|---|
| 0 < t ≤ 10 | 4 | 4 |
| 10 < t ≤ 20 | 15 | 19 |
| 20 < t ≤ 30 | 18 | 37 |
| 30 < t ≤ 40 | 22 | 59 |
2)
Plot the lower starting boundary (0,0), then each upper class boundary: .
3)
Label time (minutes) on the horizontal axis and cumulative frequency on the vertical axis. Join the points with a smooth increasing curve, as on booklet p. 69.
4)
Ans =
Plot (0,0), (10,4), (20,19), (30,37), (40,59).