Standard Deviation for 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5
s = 5.3044σ & 4.8422σ for sample & total population respectively for the dataset 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5.
The complete work with step by step calculation for 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5 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 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5?
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 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5 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 = 9.5, x2 = 13.3, . . . . , x6 = 23.5
Number of samples n = 6
Degrees of freedom = n - 1
= (6 - 1) = 5
Find sample standard deviation of 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5
step 2 Find the mean for 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5
µ =
n
∑
i = 1
Xin
=(9.5 + 13.3 + 17.5 + . . . . + 23.5)/6
µ = 15.7167
step 3 Apply the samples, mean & degrees of freedom values in the below sample standard deviation formula
=√{ (9.5 - 15.7167)² + (13.3 - 15.7167)² + (17.5 - 15.7167)² + . . . . + (23.5 - 15.7167)²}/5
= √(-6.2167)² + (-2.4167)² + (1.7833)² + . . . . + (7.7833)²/5
= √(38.6469 + 5.8403 + 3.1803 + . . . . + 60.5803)/5
= √140.6833/5
= √28.1367
s = 5.3044
For the dataset 9.5, 13.3, 17.5, 11.25, 19.25 and 23.5
15.7167 is the mean
5.3044 σ is the estimated (sample) standard deviation
28.1367 is estimated (sample) variance
4.8422 σ is the standard deviation of finite population
23.4472 is the variance of finite population
