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Likurg_2 [28]
3 years ago
5

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

Mathematics
2 answers:
Paladinen [302]3 years ago
5 0

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.


Ierofanga [76]3 years ago
4 0

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.

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