Question

Find the standard deviation of the distribution 12,6,7,3,15,10,18,5

Answer 1

Question: Find the standard deviation of the distribution 12, 6, 7, 3, 15, 10, 18, 5.

Solution:

1) Mean value $\bar{x} = \frac{12 + 6 + 7 + 3 + 15 + 10 + 18 + 5}{8} = \frac{19}{2} = 9.5$

2) $\bar{\sigma}$ - standard deviation.

$$\bar{\sigma}^2 = \frac{1}{8} \left((12 - 9.5)^2 + (6 - 9.5)^2 + (7 - 9.5)^2 + (3 - 9.5)^2 + (15 - 9.5)^2 + (10 - 9.5)^2 + (18 - 9.5)^2 + (5 - 9.5)^2\right) = \frac{1}{8} \left(2.5^2 + 3.5^2 + 2.5^2 + 6.5^2 + 5.5^2 + 0.5^2 + 8.5^2 + 4.5^2\right) = \frac{1}{8} \left(6.25 + 12.25 + 6.25 + 42.25 + 30.25 + 0.25 + 72.25 + 20.25\right) = \frac{1}{8} * 190 = \frac{95}{4}.$$ $$\bar{\sigma} = \sqrt{\frac{95}{4}} = \frac{\sqrt{95}}{2}.$$

Answer: $\bar{\sigma} = \frac{\sqrt{95}}{2} = 4.8734$.