Find the mean marks of the students using step deviation method.

| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequency | 5 | 8 | 15 | 16 | 6 |

Question

Find the mean marks of the students using step deviation method.

| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequency | 5 | 8 | 15 | 16 | 6 |

Accepted Answer

> [!TLDR] The step-deviation method scales the deviations $d_i=x_i-A$ by the common class width $h$ to keep the arithmetic small, then rescales back at the end.
>
> [!FORMULA] $\bar{x}=A+h	imes\dfrac{\sum f_iu_i}{\sum f_i}, \quad u_i=\dfrac{x_i-A}{h}$
> where $A$ = assumed mean, $h$ = class width, $x_i$ = class mark, $f_i$ = frequency.

1. **Tabulate class marks:**

| Class Interval | $f_i$ | $x_i$ |
   |---|---|---|
   | 0–10 | 5 | 5 |
   | 10–20 | 8 | 15 |
   | 20–30 | 15 | 25 |
   | 30–40 | 16 | 35 |
   | 40–50 | 6 | 45 |

2. **Choose $A=25$** (class mark of the middle class) and **class width $h=10$**.

3. **Compute $u_i=\dfrac{x_i-25}{10}$ and $f_iu_i$:**

| Class Interval | $f_i$ | $x_i$ | $u_i=\dfrac{x_i-25}{10}$ | $f_iu_i$ |
   |---|---|---|---|---|
   | 0–10 | 5 | 5 | −2 | −10 |
   | 10–20 | 8 | 15 | −1 | −8 |
   | 20–30 | 15 | 25 | 0 | 0 | …

Concept understanding — Mean

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