MATH 225 Week 3 Measures of Variation Notes
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28651209425940©2024 Chamberlain University ©2024 Chamberlain University MATH225 Skewness S Standard Deviation Range Highest Data Value – Lowest Data Value Variance 11430002080324286250385819 Steps to find Population Variance: Find the mean. (μ) Calculate the deviation of each data entry from the mean. (x - μ) Square each deviation. (x - μ)2 To help organize steps 2 – 3, create the following table: Data Values (x) Deviations (x - μ) Deviations Squared (x - μ)2 Take the sum of the squared deviations from the 3rd column. Z(x - μ)2 Divide the sum from Step 4 by N. Z(x - μ)2/N Standard Deviation To find Population Standard Deviation: 1 – 5. Same as steps above Take the square root of answer from Step 5. Example: Find the range, mean, variance, and standard deviation of the population data set. 22, 10, 6, 9, 8 Range = 16 Mean (m) = 11 x (x - μ) (x - μ)2 22 11 121 10 -1 1 6 -5 25 9 -2 4 8 -3 9 Z(x - μ)2 = 160 Z(x - μ)2/N = 160/5 = 32 Population standard deviation = 5.66 Sample variance = 160/4 = 40 Sample standard deviation = 6.32 Example: The lengths of the first 10 words of two books are listed below. Find the range, variance, and standard deviation for each of the t
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