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Statistics

Statistics. Pictograph Bar Graph Time Line Histogram Line Graph. Circle Graph Line Plot Scatter Plot Stem-and-Leaf Plot Box & Whiskers Plot. Types of Graphs. Why do we use graphs?. Creating graphs help us to organize data for research.

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Statistics

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  1. Statistics

  2. Pictograph Bar Graph Time Line Histogram Line Graph Circle Graph Line Plot Scatter Plot Stem-and-Leaf Plot Box & Whiskers Plot Types of Graphs

  3. Why do we use graphs? • Creating graphs help us to organize data for research. • We can utilize this information to make predictions and show trends.

  4. Frequency Table A way to organize data into categories or groups

  5. Measures of Central Tendency • This is a single number that represents a set of numbers. • Three common measures • Mean • Median • Mode

  6. Describe Median

  7. Median • This is the number in the middle of the data when the numbers are written in order. • Sometimes, this is the mean. Examples: • 6,8,8,9,10,12,13 = 9 • 2,2,4,6,8,8,9,10 6 + 8 = 7 2

  8. Mean

  9. Mean • Average • This is the sum of the numbers divided by how many numbers are in the set. Example: 10,10,12,14,15 10 + 10 + 12 + 14 + 15 = 12.2 5

  10. Mode

  11. Mode • This is the number that occurs most often. When all the data occurs the same amount of time , there is no mode. • There may be more than one mode. Example: 10,10,11,12,12,12,13,15 mode = 12

  12. Range The range of a set of data is the difference between the greatest and least values. Example: Data = 1,2,5,7,8 8-1=7

  13. Practice problems: • Find the mean, median, mode, and range 5, 2, 5, 6, 8, 5 6, 8, 4, 6, 3, 2

  14. Outlier • A value much greater or much less than others in a data set Example: 1,1,1,2,3,4,4,5,15

  15. Explain how an outlier affects the mean, median, and mode of a set. An outlier usually has the most affect on the mean. The median may not be affected as much because it is the data value in the middle position. The mode will not be affected at all.

  16. Most useful When • Mean: the data is spread evenly • Median: the data has an outlier • Mode: the data involve a subject in which many data points of one value are important, such as election results

  17. Practice Problems For this line plot, which measure of center would be best describe the data? Why? Answer: Median – the outlier skews the information

  18. Practice Problems For this line plot, which measure of center would be best describe the data? Why? Answer: Median – the outlier skews the information

  19. Practice Problem • The test scores of the QPA are as follows: 82, 88, 78, 90, 90, 100, 85, 75, 95, 85 Which measure of center best describes the data? Why? Answer: Mean – The data is spread evenly and there is no outlier.

  20. Practice Problem • The test scores of the QPA are as follows: 82, 88, 78, 90, 90, 100, 85, 75, 95, 85 Which measure of center best describes the data? Why? Answer: Mean – The data is spread evenly and there is no outlier.

  21. Practice Problem • During the presidential election the candidate with the most votes wins the election. Which measure of center is use to determine the best representation of the data? • Answer: Mode

  22. Practice Problem • During the presidential election the candidate with the most votes wins the election. Which measure of center is use to determine the best representation of the data? • Answer: Mode

  23. Common Uses of Data Displays

  24. Use a Bar Graph Think: is the information in the table describing a change over time? Is the information in the table divided into different categories?

  25. Stem & Leaf Plot • This is a technique for ordering data in increasing or decreasing order. Ordered Plot Unordered Plot S T E M S T E M Leaves Leaves

  26. Stem and Leaf Step 1: Group the data by tens digits. Step 2: Order the data from least to greatest. Step 3: List the tens digits of the data in order from least to greatest. Write these in the “stems” column. Step 4: For each tens digit, record the ones digits of each data value in order from least to greatest. Write these in the “leaves” column.

  27. Practice Problem Create a stem & leaf plot using the below data: 15, 10, 4, 5, 25, 36, 8, 8, 14, 35, 33, 27, 28

  28. Practice Problem Create a stem & leaf plot using the below data: 5, 10, 14, 35, 25, 16, 8, 14, 44, 33, 27, 28

  29. Answer

  30. Trivia Question What is the symbol for mean?

  31. Trivia Question x̅ What is the symbol for mean?

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