# Standard Deviation (σ) for Finite Population 78, 92, 85, 65 & 90

9.7775σ & 10.9316σ is the population and sample *standard deviation* respectively for the below distribution.

The complete work with step by step calculation to find the degree of uncertainty from its *mean* for entire population 78, 92, 85, 65 & 90 may helpful for grade school students to solve the similar worksheet problems or to understand how to do it manually.

## Workout for PSD of 78, 92, 85, 65 & 90?

The below workout with step by step calculation may help grade school students, beginners or learners to understand how to measure degree of uncertainty or standard deviation for entire population 78, 92, 85, 65 & 90 or to summarize the details of how close the linear variability of whole elements to its mean of finite population in the statistical experiments.

__Workout :__

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

Input parameters & values

x_{1} = 78, x_{2} = 92, . . . . , x_{5} = 90

Number of samples n = 5

Find standard deviation for finite population 78, 92, 85, 65 & 90

step 2 *Find the mean for 78, 92, 85, 65 & 90*

µ =
n
∑
i = 1
X_{i}n

=(78 + 92 + 85 + . . . . + 90)/5

µ = 82

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

=√{ (78 - 82)² + (92 - 82)² + (85 - 82)² + . . . . + (90 - 82)²}/5

= √(-4)² + (10)² + (3)² + . . . . + (8)²/5

= √(16 + 100 + 9 + . . . . + 64)/5

= √478/5

= √95.6

s = 9.7775

For the dataset 78, 92, 85, 65 & 90

82 is the mean

9.7775 σ is the standard deviation (σ) for finite population

95.6 is the *variance* (σ^{2}) of finite population

10.9316 σ is the estimate standard deviation (s) of population

119.5 is the estimate variance (s^{2}) of population