Relative and Cumulative Relative Frequency
POINT
Relative frequency is the frequency divided by the total. Cumulative relative frequency is the sum of relative frequencies up to that class. The final total is 1.00.
EXAMPLE
Find A–J in the table.
| Class interval | Frequency | Relative frequency | Cumulative relative frequency |
|---|---|---|---|
| 6.5–7.0 | 4 | 0.04 | 0.04 |
| 7.0–7.5 | 7 | D | F |
| 7.5–8.0 | 15 | 0.15 | G |
| 8.0–8.5 | A | 0.37 | H |
| 8.5–9.0 | 16 | E | I |
| 9.0–9.5 | B | 0.13 | J |
| 9.5–10.0 | C | 0.08 | 1.00 |
| Total | 100 | 1.00 | — |
A = 37, B = 13, C = 8, D = 0.07, E = 0.16
F = 0.11, G = 0.26, H = 0.63, I = 0.79, J = 0.92
Practice
Complete the relative frequency and cumulative relative frequency table.
01
| Class interval | Frequency | Relative frequency | Cumulative relative frequency |
|---|---|---|---|
| 6.5–7.0 | ? | 0.08 | 0.08 |
| 7.0–7.5 | 12 | ? | 0.20 |
| 7.5–8.0 | 20 | 0.20 | ? |
| 8.0–8.5 | 30 | 0.30 | 0.70 |
| 8.5–9.0 | 18 | ? | 0.88 |
| 9.0–9.5 | 7 | 0.07 | ? |
| 9.5–10.0 | 5 | 0.05 | 1.00 |
| Total | 100 | 1.00 | — |
Frequency (6.5–7.0) = 8
Relative frequency (7.0–7.5) = 0.12
Cumulative relative frequency (7.5–8.0) = 0.40
Relative frequency (8.5–9.0) = 0.18
Cumulative relative frequency (9.0–9.5) = 0.95
02
| Class interval | Frequency | Relative frequency | Cumulative relative frequency |
|---|---|---|---|
| 6.5–7.0 | 5 | 0.05 | 0.05 |
| 7.0–7.5 | ? | 0.15 | 0.20 |
| 7.5–8.0 | 25 | ? | 0.45 |
| 8.0–8.5 | 20 | 0.20 | ? |
| 8.5–9.0 | 15 | 0.15 | 0.80 |
| 9.0–9.5 | 10 | ? | 0.90 |
| 9.5–10.0 | 10 | 0.10 | ? |
| Total | 100 | 1.00 | — |
Frequency (7.0–7.5) = 15
Relative frequency (7.5–8.0) = 0.25
Cumulative relative frequency (8.0–8.5) = 0.65
Relative frequency (9.0–9.5) = 0.10
Cumulative relative frequency (9.5–10.0) = 1.00
03
| Class interval | Frequency | Relative frequency | Cumulative relative frequency |
|---|---|---|---|
| 6.5–7.0 | 10 | 0.10 | 0.10 |
| 7.0–7.5 | 8 | 0.08 | 0.18 |
| 7.5–8.0 | ? | 0.17 | 0.35 |
| 8.0–8.5 | 25 | ? | 0.60 |
| 8.5–9.0 | 20 | 0.20 | ? |
| 9.0–9.5 | 12 | 0.12 | ? |
| 9.5–10.0 | 8 | ? | 1.00 |
| Total | 100 | 1.00 | — |
Frequency (7.5–8.0) = 17
Relative frequency (8.0–8.5) = 0.25
Cumulative relative frequency (8.5–9.0) = 0.80
Relative frequency (9.5–10.0) = 0.08
Cumulative relative frequency (9.0–9.5) = 0.92
04
| Class interval | Frequency | Relative frequency | Cumulative relative frequency |
|---|---|---|---|
| 6.5–7.0 | 6 | ? | 0.06 |
| 7.0–7.5 | 14 | 0.14 | ? |
| 7.5–8.0 | 18 | 0.18 | 0.38 |
| 8.0–8.5 | ? | 0.22 | 0.60 |
| 8.5–9.0 | 16 | ? | 0.76 |
| 9.0–9.5 | 14 | 0.14 | 0.90 |
| 9.5–10.0 | 10 | 0.10 | ? |
| Total | 100 | 1.00 | — |
Frequency (8.0–8.5) = 22
Relative frequency (6.5–7.0) = 0.06
Cumulative relative frequency (7.0–7.5) = 0.20
Relative frequency (8.5–9.0) = 0.16
Cumulative relative frequency (9.5–10.0) = 1.00
05
| Class interval | Frequency | Relative frequency | Cumulative relative frequency |
|---|---|---|---|
| 6.5–7.0 | 4 | 0.04 | 0.04 |
| 7.0–7.5 | 11 | 0.11 | 0.15 |
| 7.5–8.0 | 19 | ? | 0.34 |
| 8.0–8.5 | 26 | 0.26 | ? |
| 8.5–9.0 | ? | 0.21 | 0.81 |
| 9.0–9.5 | 13 | ? | 0.94 |
| 9.5–10.0 | 6 | 0.06 | ? |
| Total | 100 | 1.00 | — |
Frequency (8.5–9.0) = 21
Relative frequency (7.5–8.0) = 0.19
Cumulative relative frequency (8.0–8.5) = 0.60
Relative frequency (9.0–9.5) = 0.13
Cumulative relative frequency (9.5–10.0) = 1.00