Class Marks and Mean
POINT
The class mark is the midpoint of a class interval. Multiply each class mark by its frequency, add the products, and divide by the total frequency to estimate the mean.
EXAMPLE
Find the class marks, calculate the products, and estimate the mean from the frequency table.
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 5–10 | 4 | ? | ? |
| 10–15 | 8 | ? | ? |
| 15–20 | 12 | ? | ? |
| 20–25 | 15 | ? | ? |
| 25–30 | 8 | ? | ? |
| 30–35 | 3 | ? | ? |
| Total | 50 | — | ? |
Practice
Find the class marks and estimated mean for each frequency table.
01
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 0–10 | 2 | ? | ? |
| 10–20 | 5 | ? | ? |
| 20–30 | 8 | ? | ? |
| 30–40 | 5 | ? | ? |
| Total | 20 | — | ? |
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 0–10 | 2 | 5 | 10 |
| 10–20 | 5 | 15 | 75 |
| 20–30 | 8 | 25 | 200 |
| 30–40 | 5 | 35 | 175 |
| Total | 20 | — | 460 |
Mean = 460 ÷ 20 = 23
02
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 10–20 | 3 | ? | ? |
| 20–30 | 7 | ? | ? |
| 30–40 | 6 | ? | ? |
| 40–50 | 4 | ? | ? |
| Total | 20 | — | ? |
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 10–20 | 3 | 15 | 45 |
| 20–30 | 7 | 25 | 175 |
| 30–40 | 6 | 35 | 210 |
| 40–50 | 4 | 45 | 180 |
| Total | 20 | — | 610 |
Mean = 610 ÷ 20 = 30.5
03
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 0–5 | 4 | ? | ? |
| 5–10 | 6 | ? | ? |
| 10–15 | 8 | ? | ? |
| 15–20 | 2 | ? | ? |
| Total | 20 | — | ? |
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 0–5 | 4 | 2.5 | 10 |
| 5–10 | 6 | 7.5 | 45 |
| 10–15 | 8 | 12.5 | 100 |
| 15–20 | 2 | 17.5 | 35 |
| Total | 20 | — | 190 |
Mean = 190 ÷ 20 = 9.5
04
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 20–30 | 5 | ? | ? |
| 30–40 | 9 | ? | ? |
| 40–50 | 4 | ? | ? |
| 50–60 | 2 | ? | ? |
| Total | 20 | — | ? |
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 20–30 | 5 | 25 | 125 |
| 30–40 | 9 | 35 | 315 |
| 40–50 | 4 | 45 | 180 |
| 50–60 | 2 | 55 | 110 |
| Total | 20 | — | 730 |
Mean = 730 ÷ 20 = 36.5
05
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 5–15 | 6 | ? | ? |
| 15–25 | 8 | ? | ? |
| 25–35 | 4 | ? | ? |
| 35–45 | 2 | ? | ? |
| Total | 20 | — | ? |
| Class interval | Frequency | Class mark | Frequency × class mark |
|---|---|---|---|
| 5–15 | 6 | 10 | 60 |
| 15–25 | 8 | 20 | 160 |
| 25–35 | 4 | 30 | 120 |
| 35–45 | 2 | 40 | 80 |
| Total | 20 | — | 420 |
Mean = 420 ÷ 20 = 21