501_Lecture_01-2

501_Lecture_01-2 - Section 1.2 Describing Distributions...

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Section 1.2 Describing Distributions with Numbers
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Quantitative Data Measuring Center Mean Median Measuring Spread Quartiles Five Number Summary Standard deviation Boxplots
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The mean The arithmetic mean of a data set (average value) Denoted by : Measures of Center x 1 2 ... 1 + + + = = n i x x x x x n n
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Mean highway mileage for the 19 2- seaters: Average: 25.8 miles/gallon Issue here: Honda Insight 68 miles/gallon! Exclude it, the mean mileage: only 23.4 mpg What does this say about the mean? Calculations 1 2 ... 24 30 . .. 30 25.8 19 + + + + + + = = = n x x x x n
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Problem: Mean can be easily influenced by outliers. It is NOT a resistant measure of center. Median Median is the midpoint of a distribution. Resistant or robust measure of center. i.e. not sensitive to extreme observations
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Mean vs. Median In a symmetric distribution, mean = median In a skewed distribution, the mean is further out in the long tail than the median. Example: house prices are usually right skewed The mean price of existing houses sold in 2000 in Indiana was 176,200. (Mean chases the right tail) The median price of these houses was only 139,000.
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Measures of spread Quartiles: Divides data into four parts (with the Median) p th percentile p percent of the observations fall at or below it. Median 50 th percentile First Quartile (Q1) 25 th percentile (median of the lower half of data) Third Quartile (Q3) 75 th percentile (median of the upper half of data)
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Calculating median Always the (n+1)/2 observation from the ordered
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501_Lecture_01-2 - Section 1.2 Describing Distributions...

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