Question

Find the sample variance and standard deviation. 20​, 10​, 5​, 6​, 12 Choose the correct answer below. Fill in the answer box to complete your choice. ​(Type an integer or a decimal. Round to one decimal place as​ needed.)

Answer 1

Answer:

mean of the sample = 10.6

mean of the standard deviation = 5.98

Step-by-step explanation:

Given data 20 10 5 6 12

The sample size is n = 5

mean:-

  Mean of the given data =∑x / n

sum of all observations and divided by 'n'

$mean (x ) = \frac{20+10+5+6+12}{5} = 10.6$

Standard deviation:-

x            x-                       ( x- mean )^2

20      20 - 10.6 = 9.4         88.36

10       10-10.6    = -0.6       0.36

5        5- 10.6  = - 5.6         31.36

6        6 - 10.6  = -4.6         21.16

12       12 - 10.6 = 1.4           1.96

                                    ∑ ( x- mean )^2 = 143.2

Sample variance s^2 = ∑(x-x)^2 / n-1

$S^{2} = \frac{143.2}{5-1} = 35.8$

The standard deviation of the sample (S) = $\sqrt{variance}$     =  5.98

conclusion:-

mean of the sample = 10.6

mean of the standard deviation = 5.98