1 / 18

Measures of Variation

zuri
Download Presentation

Measures of Variation

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. Measures of Variation Part II

    2. Coefficient of Variation Compares the standard deviation relative to the mean Written as a percent Useful for comparing data sets using different scales, such as heights and shoe sizes

    3. Formulas Samples: Populations:

    4. Example A study was done of the heights and weights of 40 men.

    5. Harry Potter reading scale Mean = 80.75 Standard deviation = 4.68

    6. Percent of scores in one standard deviation of the mean Procedure: Obtain values for mean standard deviation and for mean + standard deviation Count the number of data values in between the 2 answers Calculate the percent by dividing the answer by the number of data values

    7. Percent of scores in two standard deviations of the mean Procedure: Obtain values for mean 2 * standard deviation and for mean + 2 * standard deviation Count the number of data values in between the 2 answers Calculate the percent by dividing the answer by the number of data values

    8. Uses of the Percent of scores in one and two standard deviations of the mean

    9. Unusual scores Scores are considered to be unusual if they are: 1. less than the mean 2 standard deviations 2. more than the mean + 2 standard deviations

    10. Example: Harry Potter

    11. Normal curve or Empirical rule The normal curve is a bell shaped distribution that is used frequently in statistics. Certain phenomenon, such as IQ scores and heights of people, follow this distribution.

    13. Example: Harry Potter Does Harry Potter data match the empirical rule? Caution: With small data sets, we will not exactly match the empirical rule values.

    14. Another Example IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What percent of people have IQ scores between 70 and 130?

    15. Still another example The head circumferences of baby girls are normally distributed with a mean of 40.05 cm and a standard deviation of 1.64 cm. Between what 2 values will 99.7% of the head circumferences lie?

    16. Chebyshevs Formula For any data set, there must be at least (1-1/K2)*100% of the data within K standard deviations of the mean where K>1

    17. Chebyshevs Results For any data set, there must be at least : 75% of the scores within 2 standard deviations of the mean 89% of the scores within 3 standard deviations of the mean

    18. Example: Harry Potter Did Harry Potter follow Chebyshevs rule?

More Related