Section3-3

# Section3-3 - Measures of Variation A Bourhim Syracuse...

This preview shows pages 1–5. Sign up to view the full content.

Measures of Variation A. Bourhim Syracuse University MAT121-Fall 2011 A. Bourhim (Syracuse University) Measures of Variation MAT121-Fall 2011 1 / 12

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction It is important to know whether the data values are very spread out and whether they clump together near the center. The variance is used as a measure of how far a set of numbers are spread out from each other, and also describes how far the data values lie from the mean. In this section, we learn about range, standard deviation, variance and coefﬁcient of variation. Range Range = maximum value - minimum value . Remark The range is very easy to compute but not very useful. Example The range of 1 , 4 , 17 , 6 , 41 , 30 is range = 41 - 1 = 40 . A. Bourhim (Syracuse University) Measures of Variation MAT121-Fall 2011 2 / 12
Standard deviation Sample Standard Deviation Formula The standard deviation of a sample is s = s ( x - x ) 2 n - 1 . Or the shortcut formula s = v u u u u t n ( x 2 ) - ± x 2 n ( n - 1 ) . The variance of a sample is s 2 , the square of the standard deviation. 2 A. Bourhim (Syracuse University) Measures of Variation MAT121-Fall 2011 3 / 12

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example Consider the following sample 1 , 4 , 5 , 2 , 4 , and ﬁnd s and s 2 . To use the ﬁrst formula: 1 Find n and x . We have n = 5 and x = 1 + 4 + 5 + 2 + 4 5 = 3 . 2 . 2 For each data value x , ﬁnd the difference x - x and then square it.
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/06/2011 for the course MAT 121 taught by Professor Quinn during the Fall '08 term at Syracuse.

### Page1 / 12

Section3-3 - Measures of Variation A Bourhim Syracuse...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online