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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. Statistics Describing Data Distributions

  7. Bell Ringer: Suppose we have sample of customers that buy the following number of lollipops. 6 4 5 3 4 6 9 3 8 1 7 5 4 5 5 1 4 2 Create a box plot to display the data. Change the first data point from a 6 to a 45. What do you notice about the box plot? The summary statistics?

  8. How do you find the standard deviation? Calculate the standard deviation of the data set: 1 2 6 5 6

  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 2: 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 and standard deviation Create a box plot to display the males numbers of pairs of shoes Describe the distribution. Are there any outliers?

  15. Example 2 (continued): 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 e) Create a box plot to display the females numbers of pairs of shoes. f) Are there any outliers? g) Compare the distributions of the males and females.

  16. Data Collection Find a partner… 1. CUP STACKING Record the time it takes to stack and unstack 6 cups. Each person should perform this 2 times. Write your 2 times on the board in the appropriate male/female column 2. AGILITY TEST a) Count the number of times you can jump across a line for 10 seconds. b) Each person should perform this 2 times. c) Write your 2 times on the board in the appropriate male/female column

  17. Example 3: 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 boxplot (use calculator) c) Are there any outliers? Calculate to verify. d) Describe the distribution using Center, Unusual Features, Shape and Spread.

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