Standard Deviation (σ) for Finite Population 2, 3, 2.5, 4, 2.7, . . . . , 2.8 & 3.5
0.6198σ & 0.6533σ 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 2, 3, 2.5, 4, 2.7, 3.2, 4.1, 2.9, 2.8 & 3.5 may helpful for grade school students to solve the similar worksheet problems or to understand how to do it manually.
Workout for PSD of 2, 3, 2.5, 4, 2.7, . . . . , 2.8 & 3.5?
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 2, 3, 2.5, 4, 2.7, 3.2, 4.1, 2.9, 2.8 & 3.5 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
x1 = 2, x2 = 3, . . . . , x10 = 3.5
Number of samples n = 10
Find standard deviation for finite population 2, 3, 2.5, 4, 2.7, 3.2, 4.1, 2.9, 2.8 & 3.5
step 2 Find the mean for 2, 3, 2.5, 4, 2.7, 3.2, 4.1, 2.9, 2.8 & 3.5
µ =
n
∑
i = 1
Xin
=(2 + 3 + 2.5 + . . . . + 3.5)/10
µ = 3.07
step 3 Apply the samples, mean & number of sample values in the below population standard deviation formula
=√{ (2 - 3.07)² + (3 - 3.07)² + (2.5 - 3.07)² + . . . . + (3.5 - 3.07)²}/10
= √(-1.07)² + (-0.07)² + (-0.57)² + . . . . + (0.43)²/10
= √(1.1449 + 0.0049 + 0.3249 + . . . . + 0.1849)/10
= √3.841/10
= √0.3841
s = 0.6198
For the dataset 2, 3, 2.5, 4, 2.7, 3.2, 4.1, 2.9, 2.8 & 3.5
3.07 is the mean
0.6198 σ is the standard deviation (σ) for finite population
0.3841 is the variance (σ2) of finite population
0.6533 σ is the estimate standard deviation (s) of population
0.4268 is the estimate variance (s2) of population
