### Theory:

Let us look at an example to find standard deviation of ungrouped data by step deviation method.
Example:
The wages of six co-workers are given below.

$$250$$, $$260$$, $$270$$, $$300$$, $$310$$, $$330$$

Find its standard deviation by step deviation method.

Explanation:

Let $$n$$ represent the number of co-workers.

$$n$$ $$=$$ $$6$$

Let $$A$$ be the assumed mean, which is the middle most value.

Here, $$A$$ $$=$$ $$270$$.

Let $$c$$ be the common divisor.

Here, $$c = 10$$.

Let $$x_{i}$$ represent the wages of each worker.

 $$x_{i}$$ $$x_{i} - A$$ $$=$$ $$x_{i} - 270$$ $$d_{i} = \frac{x_{i} - A}{c}$$ $$=$$ $$\frac{x_{i} - A}{10}$$ $$d_{i}^{2}$$ $$250$$ $$-20$$ $$-2$$ $$4$$ $$260$$ $$-10$$ $$-1$$ $$1$$ $$270$$ $$0$$ $$0$$ $$0$$ $$300$$ $$30$$ $$3$$ $$9$$ $$310$$ $$40$$ $$4$$ $$16$$ $$330$$ $$60$$ $$6$$ $$36$$ $$\sum d_{i} = 10$$ $$\sum d_{i}^{2} = 66$$
The  formula to calculate the standard deviation by step deviation method is given by:

$$\sigma = c \times \sqrt{\frac{\sum d_{i}^{2}}{n}- \left(\frac{\sum d_{i}}{n}\right)^2}$$ where $$d_{i} = \frac{x_{i} - A}{c}$$.
Substitute the known values in the above formula.

$$\sigma = 10 \times \sqrt{\frac{66}{6}- \left(\frac{10}{6}\right)^2}$$

$$=$$ $$10 \times \sqrt{11 - (1.667)^2}$$

$$=$$ $$10 \times \sqrt{11 - 2.779}$$

$$=$$ $$10 \times \sqrt{8.221}$$

$$=$$ $$10 \times 2.8672$$

$$=$$ $$28.672$$

$$\approx$$ $$28.67$$

Therefore, the standard deviation of the given data is $$28.67$$.