Download presentation

Presentation is loading. Please wait.

Published byRayna Antil Modified over 3 years ago

1
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
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
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
4 (11-10) 2 (12-10) 2 (8-10) 2 (-4) 2 (0) 2 (3) 2 (-4) 2 (0) 2 (3) 2 10 13( - ) 2 13-10 10 ( - ) 2 10-10 ( - ) 2 8-1012-1011-10 6 106-10 0914416(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 = 10.0 0914416

5
5 - 1 Finding the Denominator Next, find the denominator: Sample = { 6, 10, 13, 11, 12, 8 } 123456 5 n = 6 123456 (x-x) 2 n -1 Sample variance: s 2 == 34 n -1 =666= 5 5 (x-x) 2 n -1 = 34 s 2 =

6
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
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 = 2.60768 = 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

Similar presentations

Presentation is loading. Please wait....

OK

1 Principles of Cycle Time Reduction Copyright 2000.

1 Principles of Cycle Time Reduction Copyright 2000.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on conservation of wildlife and natural vegetation Ppt on bolivian water wars Ppt on game theory youtube Ppt on different types of dance forms pdf Ppt on edge detection Convert pptx to ppt online free Ppt on issue of shares and debentures Ppt on computer network topology Ppt on acid-base indicators examples Ppt on global warming and acid rain