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Course: STAT 110, Fall 2009School: Los Angeles Southwest...
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12: Chapter Describing Distributions with Numbers We create graphs to give us a picture of the data. We also need numbers to summarize the center and spread of a distribution. Two types of descriptive statistics for categorical variables: 1) Counts (Frequencies) 2) Rates or Proportions (Relative Frequencies) Many statistics available to summarize quantitative variables. Homeruns in Baseball Question: Who is...
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12: Chapter Describing Distributions with Numbers
We create graphs to give us a picture of the data. We also need numbers to summarize the center and spread of a distribution. Two types of descriptive statistics for categorical variables:
1) Counts (Frequencies) 2) Rates or Proportions (Relative Frequencies)
Many statistics available to summarize quantitative variables.
Homeruns in Baseball
Question: Who is the best home run hitter ever in major league baseball? Players with high numbers of homeruns in seasons: Babe Ruth Roger Maris Mark McGwire Sammy Sosa Barry Bonds
1
Median and Quartiles
The median (M) is the midpoint of a distribution when the observations are arranged in increasing order. Number such that half the observations are smaller and the other half are larger. (p. 219) List the data in order from smallest to largest If n is odd, the median is the middle value. If n is even, the median is the mean of the middle two values.
M for Sosa and Maris
Calculate M for Sosa's homeruns in a season (8 seasons, to 1999). Data: 15, 10, 33, 25, 36, 40, 36, 66 Calculate M for Maris's homeruns in a season (11 seasons). Data: 14, 28, 16, 39, 61, 33, 23, 26, 13, 9, 5
2
Percentiles
p100% percentile the value of a variable such that p100% of the values are below it and (1-p)100% of the values are above it where 0 < p < 1. For the 35th percentile, p=0.35. Where have you seen percentiles before?
Quartiles
First Quartile (Q1): The value that such 25% of the data values lie below Q1 and 75% of the data values lie above Q1. (25th percentile) Third Quartile (Q3): The value such that 75% of the data values lie below Q3 and 25% of the data values lie above Q3. (75th percentile) The median is the second quartile (Q2) . (50th percentile)
3
Calculating percentiles:
Let n be the number of data values. Order the n values from largest to smallest. Calculate the product, np.
If the product is not an integer (0,1,2,3,...), then round it up to the next integer and take the corresponding ordered value. If the product is an integer, say k, then average the kth and (k+1)-st ordered values.
5-Number Summary
The 5-number summary of a data set consists of the following descriptive statistics (p. 221): Minimum, First Quartile (Q1), Median, Third Quartile (Q3), Maximum Give the 5-number summaries for Sosa and Mar...
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