Question

Which answer is the approximate standard deviation of the data set?

Answer 1

Answer: Option'D' is correct.

Step-by-step explanation:

Since we have given that

$(15,19,3,12,17,2,2,8)$

1) We will calculate the mean :

$Mean=\frac{\text{Total sum of observation}}{\text{ Number of observation}}\\\\Mean=\frac{15+19+3+12+17+2+2+8}{8}\\\\Mean=\frac{78}{5}=9.75$

2) Now, we will calculate $\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}$

so, it becomes ,

$\frac{(15-9.75)^2+(19-9.75)^2+(3-9.75)^2+(12-9.75)^2+(17-9.75)^2+(2-9.75)^2+(2-9.75)^2+(8-9.75)^2}{8-1}\\\\=\frac{339.5}{7}\\\\=48.5$

3) Take the square root of above number i.e. $\sqrt{\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}}$

$\sqrt{48.5}\\\\=6.96\\\\=7$

Hence, Option'D' is correct.

Answer 2

Answer:  A. 6.5

Step-by-step explanation:

Here, the given set = { 15, 19 3, 12, 17, 2, 2, 8}

Mean, $\overline{ x} = \frac{15+19+3+12+17+2+2+8}{8} = \frac{78}{8} = 9.75$

Number of elements, n = 8

$\frac{\sum (|x-\overline{x}|)^2}{n}=42.4375$

Thus, the standard deviation, $\sigma =\frac{\sqrt{\sum(|x-\overline{x}|)^2} }{n}=\sqrt{\frac{339.5}{8}}=\sqrt{42.4375} = 6.51440711\approx 6.5$

⇒ Option A is correct.