Question

Determine the standard deviation (c) by filling in the table as part of your calculation.

Consider the following data 6, 6, 10, 8, 10, 8
x
-
(x
- x 2
a. 1.63
b. 0.47
0.94
1.15
d.
Please select the best answer from the choices provided

Answer 1

The standard deviation
`\simeq 1.63`

Explanation:

Here, 6 values are given. Let the variable be X

Let, the values be
`x_(i)` where, i = 1(1)6

or i = 1 , 2, 3, 4, 5, 6 .

Here, the arithmetic mean is,

`\frac {\sum_(i = 1)^(6)x_(i)}{6}`

= ( 6 + 6 + 10 + 8 + 10 + 8)/6

= 8

Now,

`\frac {\sum_(i = 1)^(6)({x_(i)}^(2))}{6}`

= ( 36 + 36 + 100 + 64 + 100 + 64)/6

`\simeq 66.67`

so, variance of X

`\simeq 66.67 - 8^(2)`

= 2.67

so, standard deviation of X,

`\simeq {\sqrt {2.67}}`

`\simeq 1.634`

Hence, here, the answer is, 1.63 .