1 / 7

Finding Sample Variance & Standard Deviation

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

keelie-peck
Télécharger la présentation

Finding Sample Variance & Standard Deviation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Finding Sample Variance & Standard Deviation Using the Definition Formula • Given: The times, in seconds, required for a sample of students to perform a required task were: 6, 10, 13, 11, 12, 8 • Find: a) The sample variance, s2 b) The sample standard deviation, s

  2. The Formula - Knowing Its Parts  (x-x)2 Sample variance: s2 = x (x-x) n -1 s2 • x is “x-bar”, the sample’s mean • (x-x) is the “deviation from mean” • The calculation of a sample statistic requires the use of a formula. In this case, use: • s2 is “s-squared”, the sample variance

  3. The Formula - Knowing Its Parts (Cont’d)  (x-x)2 Sample variance: s2 = (x-x)2  (x-x)2 n -1 n -1 • (x-x)2 is the “squared deviation from the mean” •  (x-x)2 is the “sum of all squared deviations” • n -1 is the “sample size less 1” (Do you have your sample data ready to use?)

  4. Finding the Numerator  (x-x)2 s2 = = n -1 Sample = { 6, 10, 13, 11, 12, 8 } and mean x = 10.0  (x-x)2 + + + + + s2 = = n -1 + + + + + + + + + + = = = 16 0 9 1 4 4 • First, find the numerator: ( - )2 6 ( - )2 10 ( - )2 13 6-10 10 10-10 13-10 10 (11-10)2 11-10 (12-10)2 12-10 (8-10)2 8-10 10 (-4)2 (0)2 (3)2 (-4)2 (0)2 (3)2 (1)2 (1)2 (2)2 (2)2 (-2)2 (-2)2 16 0 9 1 4 4 34

  5. Finding the Denominator  (x-x)2 34 Sample variance: s2 = = n -1 n -1 = n = 6 1 2 3 4 5 6  (x-x)2 34 s2 = = n -1 • Next, find the denominator: Sample = { 6, 10, 13, 11, 12, 8 } 5 6 6 6 - 1 = 5 1 2 3 4 5 6 5

  6. Finding the Answer (a)  (x-x)2  (x-x)2 34 34 = = s2 = n -1 n -1 5 5 = s2 = • 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

  7. Finding the Standard Deviation (b) s =  s2 s =  s2 =  6.8 • The standard deviation is the square root of variance: • Therefore, the standard deviation is: = 2.60768 = 2.6 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

More Related