Measures of Variability_Ungrouped Data.pptx - Measures of Dispersion Range is the difference between the highest(H and the lowest(L data values R =

# Measures of Variability_Ungrouped Data.pptx - Measures of...

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Measures of Dispersion Range is the difference between the highest (H) and the lowest (L) data values R = H – L Deviation is the average of the difference between each data value and the mean Variance (δ 2 ) δ 2 = ∑ (x - µ) 2 N population variance s 2 = ∑ (x - x) 2 n sample variance
Measures of Dispersion Alternative Formula for Computing Variance δ 2 = N(∑x 2 ) – (∑x) 2 N 2 s 2 = n(∑x 2 ) – (∑x) 2 n(n – 1)
Standard Deviation Is the square root of the variance population standard variance sample standard variance δ 2 = ∑ (x - µ) 2 N s 2 = ∑ (x - x) 2 n
ExampleGiven the number of clients 10 employees are able to served in a day: 6, 11, 5, 1, 6, 6, 7, 5, 7, and 6. Find the range, population variance and standard deviation. Solution: 10
Example 6 + 11 + 5 + 1 + 6 + 6 + 7 + 5 + 7 + 6 10 = µ = ∑x N 60 10 = = 6
δ 2 = 54 10 = 5.4 = 2.3 δ = 5.4 Example
Another way of computing population variance δ 2 = 10(414) – (60) 2 (10) 2 = 4140 – 3600 100 = 540 100 = 5.4 δ 2 = N(∑x 2 ) – (∑x) 2 N 2
Sample Variance and Standard Deviation from Grouped Data s 2 = ∑f (x - x) 2 n - 1 or s 2 = n(∑x 2 f) – (∑xf) 2 n(n – 1) sd = ∑f (x - x) 2 n - 1 sd = n(∑x 2 f) – (∑xf) 2 n(n – 1)