# Standard Deviation for 3, 6, 9, 12, 15, 18, 21, 24 and 27

s = 8.2158σ & 7.746σ for sample & total population respectively for the dataset 3, 6, 9, 12, 15, 18, 21, 24 and 27.

The complete work with step by step calculation for 3, 6, 9, 12, 15, . . . . , 24 and 27 may helpful for grade school students, beginners or learners to solve the similar standard deviation worksheet problems to estimate the degree of uncertainty, or how much the whole members in a group deviates from its *mean* or common behavior of sample data distribution, to draw the conclusions of population data distribution to improve the quality of process.

## Estimate Degree of Uncertainty for 3, 6, 9, 12, 15, 18, 21, 24 and 27?

The below workout with step by step work or calculation may help users to understand how to estimate what is the standard deviation for the data set 3, 6, 9, 12, 15, . . . . , 24 and 27 to summarize the degree of uncertainty or linear variability of whole elements in a group of sample elements, to draw the conclusion about the characteristics of population data in the statistical experiments.

__Workout :__

step 1 Address the *formula*, input parameters & values

Input parameters & values

x_{1} = 3, x_{2} = 6, . . . . , x_{9} = 27

Number of samples n = 9

Degrees of freedom = n - 1

= (9 - 1) = 8

Find sample standard deviation of 3, 6, 9, 12, 15, 18, 21, 24 and 27

step 2 *Find the mean for 3, 6, 9, 12, 15, 18, 21, 24 and 27*

µ =
n
∑
i = 1
X_{i}n

=(3 + 6 + 9 + . . . . + 27)/9

µ = 15

step 3 Apply the samples, mean & degrees of freedom values in the below sample standard deviation formula

=√{ (3 - 15)² + (6 - 15)² + (9 - 15)² + . . . . + (27 - 15)²}/8

= √(-12)² + (-9)² + (-6)² + . . . . + (12)²/8

= √(144 + 81 + 36 + . . . . + 144)/8

= √540/8

= √67.5

s = 8.2158

For the dataset 3, 6, 9, 12, 15, 18, 21, 24 and 27

15 is the mean

8.2158 σ is the estimated (sample) standard deviation

67.5 is estimated (sample) *variance*

7.746 σ is the standard deviation of finite population

60 is the variance of finite population