1 Finding Sample Variance & Standard Deviation  Given: The times, in seconds, required for a sample of students to perform a required task were:  Find: a) The sample variance, s 2 6,10,13,11,12,8 b) The sample standard deviation, s Using the Definition Formula

2  The calculation of a sample statistic requires the use of a formula. In this case, use:  (x-x) 2 n -1 Sample variance: s 2 = The Formula - Knowing Its Parts s 2 is “s-squared”, the sample variance (x-x) is the “deviation from mean” x is “x-bar”, the sample’s mean x s2s2 (x-x)

3 Sample variance: s 2 =  (x-x) 2 n -1 (x-x) 2 The Formula - Knowing Its Parts (Cont’d) (Do you have your sample data ready to use?) n -1 is the “sample size less 1”  (x-x) 2 is the “sum of all squared deviations” (x-x) 2 is the “squared deviation from the mean”  (x-x) 2 n -1

4 (11-10) 2 (12-10) 2 (8-10) 2 (-4) 2 (0) 2 (3) 2 (-4) 2 (0) 2 (3) ( - ) ( - ) ( - ) (1) 2 (2) 2 (-2) 2  First, find the numerator: Finding the Numerator =  (x-x) 2 n -1 s 2 = =  (x-x) 2 n -1 s 2 = (1) 2 (2) 2 (-2) 2 = = = 34 Sample = { 6, 10, 13, 11, 12, 8 } and mean x =

5 - 1 Finding the Denominator  Next, find the denominator: Sample = { 6, 10, 13, 11, 12, 8 } n =  (x-x) 2 n -1 Sample variance: s 2 == 34 n -1 =666= 5 5  (x-x) 2 n -1 = 34 s 2 =

6 Finding the Answer (a)  Lastly, divide and you have the answer! 6.8 The sample variance is 6.8 Note: Variance has NO unit of measure, it’s a number only 5  (x-x) 2 n -1 = 34 s 2 = = 5  (x-x) 2 n -1 = 34 s 2 =

7 Finding the Standard Deviation (b)  The standard deviation is the square root of variance: s =  s 2  Therefore, the standard deviation is: s =  s 2 =  6.8 = = The standard deviation of the times is 2.6 seconds Note: The unit of measure for the standard deviation is the unit of the data 2.6