1 / 13

Chapter 3 – Data Description section 3.3 –Measures of Position

Chapter 3 – Data Description section 3.3 –Measures of Position. Measures of Position Z-Scores. Different data sets can have vastly different characteristics. ( apples and oranges ) Z-Scores allow us to compare them.

leverett-reynaud
Download Presentation

Chapter 3 – Data Description section 3.3 –Measures of Position

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. Chapter 3 – Data Descriptionsection 3.3 –Measures of Position

  2. Measures of PositionZ-Scores • Different data sets can have vastly different characteristics. (apples and oranges) • Z-Scores allow us to compare them. • a z-score (or standard score) for a value is obtained by subtracting the mean from the value and dividing the result by the standard deviation.

  3. Measures of PositionZ-Scores Example: • a student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10. • She scored 30 on a history test with a mean of 25 and a standard deviation of 5. • Compare her relative positions for the two tests

  4. Measures of PositionPercentiles • Percentiles divide the data set into 100 equal parts. • SAT Score Reports usually give percentiles scores • a percentile score of 73 means that you did better than 73 percent of everyone who took the test at the same time as you. • Percentile graphs are similar to Ogives • take a look at the graph on page 133…

  5. Measures of PositionPercentiles The percentile corresponding to a given value X is computed by using the following formula:

  6. Measures of PositionPercentiles Example • A teacher give a 20-point quiz to 10 students. Here are the scores: 18, 15, 12, 6, 8, 2, 3, 5, 20, 10 • Find the percentile rank for a score of 12. • So the kid who scored 12 did better than 65% of the class. • find the percentile rank for a score of 6.

  7. Measures of PositionPercentiles Example • A teacher give a 20-point quiz to 10 students. Here are the scores: 18, 15, 12, 6, 8, 2, 3, 5, 20, 10 • Using the same data, find the score corresponding to the 25th percentile. • what about the 60th percentile?

  8. Measures of PositionPercentiles Going backwards is a little different: • Arrange the data from lowest to highest • substitute into the formula c = np/100 where: • n = total number of values • p = percentile • If c is not a whole number, round up to the next whole number. Count up to that number. • If c is a whole number, average the cth and (c+1)th values.

  9. Measures of PositionPercentiles Example • A teacher give a 20-point quiz to 10 students. Here are the scores: 18, 15, 12, 6, 8, 2, 3, 5, 20, 10 • Using the same data, find the score corresponding to the 25th percentile. • what about the 60th percentile?

  10. Measures of PositionQuartiles • Quartiles divide the data into quarters. • We call the quartiles Q1, Q2, Q3 • First find the median • this is Q2 • Next find the “median” of the data that falls below Q2 • this is Q1 • Finally, find the “median” of the data that falls above Q2 • this is Q3

  11. Measures of PositionQuartiles • The Inter-quartile range (IQR) is another useful measure of variability. • IQR = Q3 – Q1 • This is the range of the middle 50% of the data. • we discussed resistant measures. • is the IQR resistant? • calculate the IQR for the quiz data.

  12. Measures of PositionOutliers • an outlier is an extremely high or low data value when compared to the rest of the data values. • Outliers are: • Data values smaller than Q1 – 1.5(IQR) • Data values larger than Q3 + 1.5(IQR) • Check this set for outliers: • 5, 6, 12, 13, 15, 18, 22, 50

  13. Practice • page 141 #1 – 29 odd!

More Related