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Chapter 12, Part 1

Chapter 12, Part 1. STA 200 Summer I 2011. Measures of Center and Spread. Measures of Center: median mean Measures of Spread: quartiles & five number summary standard deviation. Median. The median is the midpoint of a distribution.

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Chapter 12, Part 1

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  1. Chapter 12, Part 1 STA 200 Summer I 2011

  2. Measures of Center and Spread • Measures of Center: • median • mean • Measures of Spread: • quartiles & five number summary • standard deviation

  3. Median • The median is the midpoint of a distribution. • In other words, it’s the number such that half of the observations are smaller and the other half are larger.

  4. Calculating the Median • Put all of the observations in order. • If the number of observations (n) is odd, the median is the observation in the middle of the list. • In general, the median can be found by counting observations up from the bottom of the list. • If the number of observations (n) is even, the median is the average of the two central observations.

  5. Example • From 1991 to 1999, the total precipitation in Lexington was, to the nearest inch: • Find the median.

  6. Another Example • In the first 16 days of May 2011, the recorded high temperatures in Lexington were: • Find the median.

  7. Quartiles • The quartiles help to give the spread of a distribution. • If the median is used to measure center, the quartiles should be used to measure spread. • There are two of them: the first quartile and the third quartile. • The quartiles (along with the median) divide the observations into quarters.

  8. Calculating the Quartiles • Put the observations in order, and determine the median. • The first quartile (Q1) is the median of the observations less than the overall median. The first quartile will be above 25% of the data. • The third quartile (Q3) is the median of the observations greater than the overall median. The third quartile will be above 75% of the data.

  9. Precipitation Example • Find the first and third quartiles for the precipitation data:

  10. Temperature Example • Find the first and third quartiles for the temperature data:

  11. Five Number Summary & Box Plot • In order to get a good idea of the distribution (center and spread), we use what is called a five number summary, and construct a graph called a box plot.

  12. Five Number Summary • The five-number summary consists of the median, quartiles, and the largest and smallest observations. • These are typically written out in increasing order: min Q1 M Q3 max (Note: M = median)

  13. Box Plot • The box plot (or box-and-whisker plot) is a graph of the five number summary. • How to construct a box plot: • a box extends from the first quartile to the third quartile • a line in the box marks the median • lines extend from the sides of the box to the smallest and largest observations

  14. Precipitation Example • For the precipitation data, determine the five number summary and construct a box plot.

  15. Temperature Example • For the temperature data, determine the five number summary and construct a box plot.

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