Mathematics: Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 2, 6, 15, 9, 11, 22, 1, 4, 8,19 A. 6.3 B. 7.1 C. 6.8 D. 2.1

Find the sample standard deviation for the given

Ответ:

sophie5064

20.01.2022

Mathematics

So, the sample standard deviation is 7.1.

Step-by-step explanation:

From Exercise we have the next numbers: 2, 6, 15, 9, 11, 22, 1, 4, 8,19.

So, N=10, because we have 10 numbers.

We use the formula for standard deviation:

$\sigma=\sqrt{\frac{1}{N-1}\cdot \sum_{i=1}^{N} (x_i-\mu)^2$

So, μ is the mean of all our values.

We get:

$\mu=\frac{2+6+15+9+11+22+1+4+8+19}{10}\\\\\mu=\frac{97}{10}\\\\\mu=9.7$

Now, we calculate the sum

$\sum_{i=1}^{10} (x_i-9.7)^2=(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2\\\\\sum_{i=1}^{10} (x_i-9.7)^2=452.1$

Therefore, we get

$\sigma=\sqrt{\frac{1}{N-1}\cdot \sum_{i=1}^{N} (x_i-\mu)^2}\\\\\sigma=\sqrt{\frac{1}{10-1}\cdot 452.1}\\\\\sigma=7.087\\\\\sigma=7.1\\$

So, the sample standard deviation is 7.1.

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Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 2, 6, 15, 9, 11, 22, 1, 4, 8,19

A. 6.3
B. 7.1
C. 6.8
D. 2.1

Ответ:

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