1. Find the mean of the distribution :
| Class | 1–3 | 3–5 | 5–7 | 7–10 |
|---|---|---|---|---|
| Frequency | 9 | 22 | 27 | 17 |
5.5
Step 1: Find the class marks (x).
The class mark is the middle point of each class interval.
Step 2: Make a table of f × x.
| Class | Frequency (f) | Class mark (x) | f × x |
|---|---|---|---|
| 1–3 | 9 | 2 | 18 |
| 3–5 | 22 | 4 | 88 |
| 5–7 | 27 | 6 | 162 |
| 7–10 | 17 | 8.5 | 144.5 |
| Total | 75 | — | 412.5 |
Step 3: Use the formula of mean.
The formula is: \(\bar{x} = \dfrac{\sum f x}{\sum f}\)
Here, \(\sum f = 75\), and \(\sum f x = 412.5\).
Step 4: Put the values.
\(\bar{x} = \dfrac{412.5}{75} = 5.5\)
Final Answer: The mean of the distribution is 5.5.