Standard Deviation for 6.7, 7.5, 9.2 and 7.3
s = 1.072σ and 0.9284σ for sample and total population respectively for the dataset 6.7, 7.5, 9.2 and 7.3.
The complete workout with step-by-step calculations for 6.7, 7.5, 9.2 and 7.3 may be 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 6.7, 7.5, 9.2 and 7.3?
The step-by-step workout below demonstrates how to estimate the standard deviation for the dataset 6.7, 7.5, 9.2 and 7.3 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 and values
Input parameters and values
x1 = 6.7, x2 = 7.5, . . . . , x4 = 7.3
Number of samples n = 4
Degrees of freedom = n - 1
= (4 - 1) = 3
Find sample standard deviation of 6.7, 7.5, 9.2 and 7.3
step 2 Find the mean for 6.7, 7.5, 9.2 and 7.3
µ =
n
∑
i = 1
Xin
=(6.7 + 7.5 + 9.2 + 7.3)/4
µ = 7.675
step 3 Apply the samples, mean & degrees of freedom values in the below sample standard deviation formula
=√{ (6.7 - 7.675)² + (7.5 - 7.675)² + (9.2 - 7.675)² + (7.3 - 7.675)²}/3
= √(-0.975)² + (-0.175)² + (1.525)² + (-0.375)²/3
= √(0.9506 + 0.0306 + 2.3256 + 0.1406)/3
= √3.4475/3
= √1.1492
s = 1.072
For the dataset 6.7, 7.5, 9.2 and 7.3
7.675 is the mean
1.072 σ is the estimated (sample) standard deviation
1.1492 is estimated (sample) variance
0.9284 σ is the standard deviation of finite population
0.8619 is the variance of finite population
