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Statistics

Statistics. Summary Statistics & Data Displays. Summary Statistics calculated from a data set: Mean – Median – Mode – Range – Minimum – Maximum – Quartile 1 – Quartile 3 – Interquartile Range – Standard Deviation – . Average of the numbers. Middle number. # that occurs the most.

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Statistics

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  1. Statistics Summary Statistics & Data Displays

  2. Summary Statistics calculated from a data set: Mean – Median – Mode – Range – Minimum – Maximum – Quartile 1 – Quartile 3 – Interquartile Range – Standard Deviation – Average of the numbers Middle number # that occurs the most maximum – minimum smallest number largest number Q1 = 1st 25% of the data Q3 = 1st 75% of the data IQR = Q3 – Q1 Measures the average distance of observations from their mean

  3. Displaying Quantitative Data Histograms – uses bars to show the distribution; each bar represents the frequency of values falling into each bin

  4. Displaying Quantitative Data 2. Box Plot – displays the 5-number summary as a central box with whiskers 5-number summary: min, Q1, Median, Q3, max

  5. Example 1: Here are the travel times in minutes for 15 workers in North Carolina. 20 10 40 25 20 10 60 15 40 5 30 12 10 10 Find the mean, median, mode, Q1, Q3, Range, IQR, minimum, maximum Create a histogram of the travel times using a bin width of 10 minutes. Create a box plot of the travel times

  6. Example 2: Suppose we have sample of customers that buy the following number of lollipops. 2 4 5 3 4 6 9 3 8 1 7 5 4 5 5 1 4 6 Find the mean, median, mode, Q1, Q3, Range, IQR, minimum, maximum Create a histogram of the purchases using a bin width of 2 lollipops Create a box plot of the purchased lollipops

  7. Standard Deviation-the average distance each observation is from their mean How do you find standard deviation? Find the standard deviation of the following set of data. 2 4 5 6 8

  8. Statistics Describing Data Distributions

  9. Describing a Distribution C – Center U – Unusual Features S – Shape S – Spread Center a) Median b) Mean

  10. Describing a Distribution 2. Unusual Features a) outliers – extreme values that don’t seem to belong Low Outlier: any data values < Q1 - 1.5*IQR High Outlier: any data values > Q3 + 1.5 * IQR b) gaps – a region where there are no data values c) clusters – the data appear to be grouped together

  11. Describing a Distribution 3. Shape a) Symmetric b) Skewed (left or right) c) Uniform

  12. Describing a Distribution 4. Spread – how spread out the data is a) IQR b) Standard Deviation

  13. If the distribution is… Symmetric: use mean & standard deviation Skewed: use median and IQR

  14. Example 3: Here are the numbers of pairs of shoes reported by each male in Mrs. Nelson’s class 14 7 6 5 12 38 8 7 10 10 10 11 4 5 22 7 5 10 35 7 Find the mean, median, mode, range, Q1, Q3, IQR, min, max Create a box plot to display the males numbers of pairs of shoes Are there any outliers? Describe the distribution

  15. Example 4: Mrs. Nelson also asked the females how many pairs of shoes they owned. Below is their data. 10 15 20 32 25 30 14 27 19 35 15 29 42 a) Create a box plot to display the females numbers of pairs of shoes. b) Are there any outliers? c) Compare the distributions of the males and females.

  16. Example 5: For an agility test, 4th graders jump side-to-side across a set of parallel lines, counting the # of times they clear in 30 seconds. Here are their scores: 22 17 18 29 22 22 23 24 23 17 21 25 20 12 28 24 22 21 25 26 25 16 19 27 a) Find the mean, 5-number summary, and standard deviation. b) Make a histogram (use calculator) c) Describe the distribution using Center, Unusual Features, Shape and Spread. d) Suppose the last data point wasn’t a 27, but really a 65…re-do parts a and b. What do you notice?

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