Find the **standard deviation** of the following data (rounded off to two decimal places):

5, 3, 4, 7

Question

Find the **standard deviation** of the following data (rounded off to two decimal places):

5, 3, 4, 7

Accepted Answer

**Solution:**

1. Calculate the mean ($\bar{x}$):
   $$
   \bar{x} = \frac{5 + 3 + 4 + 7}{4} = \frac{19}{4} = 4.75
   $$

2. Calculate the squared differences from the mean:
   - $(5 - 4.75)^2 = (0.25)^2 = 0.0625$
   - $(3 - 4.75)^2 = (-1.75)^2 = 3.0625$
   - $(4 - 4.75)^2 = (-0.75)^2 = 0.5625$
   - $(7 - 4.75)^2 = (2.25)^2 = 5.0625$

3. Calculate the variance ($\sigma^2$):
   $$
   \sigma^2 = \frac{0.0625 + 3.0625 + 0.5625 + 5.0625}{4} = \frac{8.75}{4} = 2.1875
   $$

4. Calculate the standard deviation ($\sigma$):
   $$
   \sigma = \sqrt{2.1875} \approx 1.478986
   $$

5. Round to two decimal places:
   $$
   1.48
   $$

**Answer:** $1.48$

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