Standard Deviation for 4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9 and 5
s = 0.3162σ & 0.2982σ for sample & total population respectively for the dataset 4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9 and 5.
The complete work with step by step calculation for 4.1, 4.2, 4.3, 4.5, 4.6, . . . . , 4.9 and 5 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 4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9 and 5?
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 4.1, 4.2, 4.3, 4.5, 4.6, . . . . , 4.9 and 5 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 = 4.1, x2 = 4.2, . . . . , x9 = 5
Number of samples n = 9
Degrees of freedom = n - 1
= (9 - 1) = 8
Find sample standard deviation of 4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9 and 5
step 2 Find the mean for 4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9 and 5
µ =
n
∑
i = 1
Xin
=(4.1 + 4.2 + 4.3 + . . . . + 5)/9
µ = 4.5667
step 3 Apply the samples, mean & degrees of freedom values in the below sample standard deviation formula
=√{ (4.1 - 4.5667)² + (4.2 - 4.5667)² + (4.3 - 4.5667)² + . . . . + (5 - 4.5667)²}/8
= √(-0.4667)² + (-0.3667)² + (-0.2667)² + . . . . + (0.4333)²/8
= √(0.2178 + 0.1344 + 0.0711 + . . . . + 0.1878)/8
= √0.8/8
= √0.1
s = 0.3162
For the dataset 4.1, 4.2, 4.3, 4.5, 4.6, 4.7, 4.8, 4.9 and 5
4.5667 is the mean
0.3162 σ is the estimated (sample) standard deviation
0.1 is estimated (sample) variance
0.2982 σ is the standard deviation of finite population
0.0889 is the variance of finite population
