1 / 12

Variance and Standard Deviation (2) Scaling

Variance and Standard Deviation (2) Scaling. Fred tries out Laxo Laxative - and finds his visits increase by 5 a day. Mean = 8.1. Mean = 13.1. 5 more visits per day, Sum is 12x5 (60) more = 157 mean is 5 more. 13.1. Sum = 97. Standard Deviation.

astrid
Télécharger la présentation

Variance and Standard Deviation (2) Scaling

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. Variance and Standard Deviation (2)Scaling

  2. Fred tries out Laxo Laxative- and finds his visits increase by 5 a day

  3. Mean = 8.1 Mean = 13.1 5 more visits per day, Sum is 12x5 (60) more = 157 mean is 5 more 13.1 Sum = 97

  4. Standard Deviation The mean will be increased by the same value The new mean becomes x + b Standard Deviation = (xi - x)2 n Sx =((xi+b) - (x+b))2 =(xi + b- x - b)2 n n If each piece of data (xi) is increased by a value, say b Each value becomes xi + b The ‘b’s just cancel and you are left will the original formula

  5. Fred’s Example Deviations from mean will be the same before and after - so the Standard Deviation and Variance must be the same

  6. Fred tries out Quixo Laxative- and finds his visits doubling

  7. Mean = 8.1 Mean = 16.2 Twice the visits per day, Sum is doubled = 194 So, the mean is doubled Sum = 97

  8. Standard Deviation The mean will be increased by the same factor The new mean becomes ax Standard Deviation = (xi - x)2 n Sx =(axi- ax)2 =a2 (xi - x)2 =a(xi - x)2 n n n If each piece of data (xi) is increased by a factor, say a Each value becomes axi The Standard Deviation is Scaled by the factor a

  9. Fred’s Example The Standard Deviation has increased by a factor of 2

  10. Summary The new mean y = ax + b • If all values are increased by adding the same value • The mean increases by that value • The Standard Deviation remains the same • If all values are multiplied by the same value • The mean is multiplied by that value • The Standard Deviation is also multiplied by this value In general, if a variable x is transformed using the linear transformation ‘y = ax + b’ The new Standard Deviation Sy = aSx

  11. Example The linear transformation ‘y = ax + b’ and Sy = aSx y = ax + b x = 21.5 , Sx = 6.4 • A test is marked out of 30 • The mean mark is 21.5 • The Standard Deviation is 6.4 • To make it into a percentage the teacher decides to multiply the marks by 3 and add 10. • What are the new mean and Standard Deviation? New mean = 3 x 21.5 + 10 = 74.5 s.d. = 3 x 6.4 = 19.2

  12. Activity Page 28 of your Statistics 1 book and try … • Exercise 1F • Scaling

More Related