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Standard Deviation for 997, 999, 995, 999, 998, 996, 998 and 997

Standard Deviation Calculator

s = 1.4079σ & 1.317σ for sample & total population respectively for the dataset 997, 999, 995, 999, 998, 996, 998 and 997.
The complete work with step by step calculation for 997, 999, 995, 999, 998, 996, 998 and 997 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 997, 999, 995, 999, 998, 996, 998 and 997?

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 997, 999, 995, 999, 998, 996, 998 and 997 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
x1 = 997, x2 = 999, . . . . , x8 = 997
Number of samples n = 8
Degrees of freedom = n - 1
= (8 - 1) = 7
Find sample standard deviation of 997, 999, 995, 999, 998, 996, 998 and 997

step 2 Find the mean for 997, 999, 995, 999, 998, 996, 998 and 997

µ = n i = 1 Xin
=(997 + 999 + 995 + . . . . + 997)/8
µ = 997.375

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

Formula to Calculate Sample Standard Deviation

=√{ (997 - 997.375)² + (999 - 997.375)² + (995 - 997.375)² + . . . . + (997 - 997.375)²}/7

= (-0.375)² + (1.625)² + (-2.375)² + . . . . + (-0.375)²/7

= (0.1406 + 2.6406 + 5.6406 + . . . . + 0.1406)/7

= 13.875/7

= √1.9821

s = 1.4079

For the dataset 997, 999, 995, 999, 998, 996, 998 and 997
997.375 is the mean
1.4079 σ is the estimated (sample) standard deviation
1.9821 is estimated (sample) variance
1.317 σ is the standard deviation of finite population
1.7344 is the variance of finite population

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