# Standard Deviation for 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1

s = 0.0794σ & 0.0742σ for sample & total population respectively for the dataset 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1.

The complete work with step by step calculation for 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1 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 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1?

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 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1 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} = 11.2, x_{2} = 11.2, . . . . , x_{8} = 11.1

Number of samples n = 8

Degrees of freedom = n - 1

= (8 - 1) = 7

Find sample standard deviation of 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1

step 2 *Find the mean for 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1*

µ =
n
∑
i = 1
X_{i}n

=(11.2 + 11.2 + 11.3 + . . . . + 11.1)/8

µ = 11.2125

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

=√{ (11.2 - 11.2125)² + (11.2 - 11.2125)² + (11.3 - 11.2125)² + . . . . + (11.1 - 11.2125)²}/7

= √(-0.0125)² + (-0.0125)² + (0.0875)² + . . . . + (-0.1125)²/7

= √(0.0002 + 0.0002 + 0.0077 + . . . . + 0.0127)/7

= √0.0438/7

= √0.0063

s = 0.0794

For the dataset 11.2, 11.2, 11.3, 11.35, 11.2, 11.15, 11.2 and 11.1

11.2125 is the mean

0.0794 σ is the estimated (sample) standard deviation

0.0063 is estimated (sample) *variance*

0.0742 σ is the standard deviation of finite population

0.0055 is the variance of finite population