2 4 measures of variation
Download
Skip this Video
Download Presentation
2.4 Measures of Variation

Loading in 2 Seconds...

play fullscreen
1 / 25

2.4 Measures of Variation - PowerPoint PPT Presentation


  • 99 Views
  • Uploaded on

2.4 Measures of Variation. The Range of a data set is simply: Range = (Max. entry) – (Min. entry). Deviation. The deviation of an entry, x , is the difference between the entry and the mean, , of the data set. Mean = Deviation of x = x - . Population Variance.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' 2.4 Measures of Variation' - hannibal-braden


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
2 4 measures of variation

2.4 Measures of Variation

The Range of a data set is simply:

Range = (Max. entry) – (Min. entry)

deviation
Deviation
  • The deviation of an entry, x, is the difference between the entry and the mean, , of the data set.
  • Mean =
  • Deviation of x = x - 
population variance
Population Variance
  • We are not going to be talking much about the Population Variance. We will be talking more about the Sample Variance.
  • Population Variance is found by:
    • Find the mean of the population  (note the symbol)
    • Find the deviation of each point by subtracting the mean from each data point
    • Square the differences
    • Add all the squares up
    • Divide by the total number of data points in the population
  • Population Variance:
population standard deviation
Population Standard Deviation
  • The Population Standard Deviation is the square root of the Population Variance.
sample variance
Sample Variance
  • We will be talking mostly about the Sample Variance.
  • Why?
  • Sample Variance is found by:
    • Find the mean of the sample:
    • Find the deviation by subtracting the mean of the sample from each data point
    • Square the differences
    • Add all the squares up
    • Divide by the total number of data points in the sample minus 1.
  • Sample Variance:
sample standard deviation
Sample Standard Deviation
  • The Sample Standard Deviation is the square root of the Sample Variance.
example
Example
  • Find the standard deviation of the following sample:
example1
Example
  • Find the standard deviation of the following sample:
example2
Example
  • Find the standard deviation of the following sample:
example3
Example
  • Find the standard deviation of the following sample:
example4
Example
  • Find the standard deviation of the following sample:

What will be the sum of this column?

example5
Example
  • Find the standard deviation of the following sample:

What will be the sum of this column?

It will always be zero

example6
Example
  • Find the standard deviation of the following sample:
example7
Example
  • Find the standard deviation of the following sample:
standard deviation
Standard Deviation
  • The TI calculators can calculate both standard deviations quickly:
    • Stats
    • Calc
    • 1-Var Stats
    • Enter the list you want to use
    • Enter
standard deviation1
Standard Deviation
  • This gives:
    • The mean of the data:
    • The sum of all of the data:
    • The sum of the squares of all the data:
    • Sample standard deviation:
    • Population standard deviation:
    • The number of data points:
    • The smallest data point value: minX
    • Etc.
standard deviation2
Standard Deviation
  • What does Standard Deviation represent?
  • It is a measure of the distance from the mean.
  • It is a measure of how far the data is from the mean.
  • It is a measure of the spread of data.
  • The larger the Standard Deviation, the more spread out the data is.
standard deviation3
Standard Deviation
  • Calculate the mean, range, and standard deviations for 8 units at a value of 7:
    • Mean = 7
    • Range = 0
    • Population and Sample Standard Deviations = 0, why?
    • There is no spread in the data. It is all the exact same number
standard deviation4
Standard Deviation
  • Calculate the mean, range, and standard deviations for 4 units each at 6 and 8:
    • Mean = 7
    • Range = 2
    • Population Standard deviation = 1, why?
    • The data is an average of one unit from the mean
    • Sample Standard Deviation = 1.069, why?
    • We are dividing by (n-1)
standard deviation5
Standard Deviation
  • Calculate the mean, range, and sample standard deviation for 2 units each at 4, 6, 8 and 10:
    • Mean = 7
    • Range = 6
    • Sample Standard deviation = 2.39 and

Population Standard Deviation = 2.236, why not 2?

    • Even though the data is an average of 2 units from the mean, the standard deviations are not exactly 2 because we are working with the square of the distances.
standard deviation summary
Standard Deviation Summary
  • Standard deviation is the square root of variance
  • Population standard deviation has an “n” in the denominator
  • Sample standard deviation has an “n – 1” in the denominator
  • Both standard deviations is a measure of the spread of data
  • The more the spread, the larger the standard deviation
standard deviation in a normal curve from http allpsych com researchmethods images normalcurve gif
Standard Deviation in a Normal Curvefrom http://allpsych.com/researchmethods/images/normalcurve.gif
slide23
Standard Deviation in a Normal Curvefrom http://www.comfsm.fm/~dleeling/statistics/normal_curve_diff_sx.gif
class work
Class Work
  • Pg 79, # 16, 18, 24
homework
Homework
  • Page 78, #
    • 5 – 9 all,
    • 13 – 21 odd,
    • 22
    • 25 & 26
    • Total of 13 problems
ad