Instructions: Copy ALL notes and sample problems into binder. View the notes as “presentation view” (as a slideshow). Some example problems you will have to work out. SHOW ALL WORK IN BINDER! Notes will be checked on Monday (for a grade). Please remember your manners and be respectful! Enjoy your weekend

5/13/ F Appropriate Data Measures

Use mean, median, or mode when… mean-the data has NO extreme values (no outliers) median-the data has extreme values (contains outliers) -there are no big gaps in the middle of the data modethe data has many repeated numbers *mean, median, mode, & range are known as measures of central tendency

Example 1 The total number of sea turtles observed at four sea turtle research sites on the eastern coast of Florida is shown below. Which measure of central tendency best represents the data? Then find that value. 1,033 ; 207 ; 1332 ; 1231

mean – cannot use the mean because the data contains extreme values (outliers) mode – cannot use the mode because there are no inputs that repeat median- most appropriate measure since there are outliers

1,033 ; 207 ; 1332 ; 1231 Now find the median: 207 ; 1033 ; 1231 ; /2 = 1132

Example 2 The numbers represent the number of threatened species in the US in Identify the outlier in the data set. 11, 13, 9, 43, 8, 11, 9 Determine how the outlier affects the: – mean – median – mode HINT: find the mean, median, and mode with the outlier included. THEN find the mean, median, and mode with the outlier excluded. See what measure is affected by the outlier.

Your Turn Identify the measure of central tendency that best represents the data. Justify your selection (explain why you picked that measure). Then calculate that measure of central tendency. There can be multiple measures that are appropriate. 1.) 100, 110, 90, 100, 100, ) 70, 80, 90

5/13/ A Select the Appropriate Display

Method:

Example 1 Which display allows you to see whether or not the number of injuries has steadily declined since 2005?

The line plot does not show the years so you cannot tell whether the number of injuries has declined. The line graph shows the number of injuries and the year they occurred. It shows that the injuries have steadily declined since 2005 except for a slight increase in So, the line graph shows the change in the number of injuries from year to year, with an overall decline in the number of injuries.

Example 2 The table shows the number of members in the school orchestra from 2005–2009. Select an appropriate type of display to compare the number of students in the orchestra over the years. These data show the number of students in the orchestra each year. Change over a period of time is best shown in a line graph. Since the table shows change over a period of time, a line graph would be best type of display.

Example 3 The table shows the number of members in the school orchestra from 2005–2009. Make the appropriate display of the data.

Step 1Draw and label horizontal and vertical axes. The horizontal axis represents the year. The vertical axis represents the number of students. Add a title.

Step 2Plot a point for the number of students for each year. Connect the points.

Your Turn

5/13/ C Misleading Graphs & Statistics

Example 1 The line graphs below show the last 10 weeks of sales for the Crumby Cookie Bakery. Do the graphs show the same data? If so, explain how the graphs differ. Which graph makes it appear that the bakery's sales declined only slightly?

The graphs show the same data, but the scale of Graph has greater intervals and a greater range. Graph A makes it appear that the bakery's sales declined only slightly.

Example 2 A.same data; intervals on the graphs are different B.same data; data in Graph A is graphed incorrectly C.same data; scale in Graph B is not consistent D.different data The graphs show the number of wins by four different soccer teams. Do the graphs show the same data? If so, explain how they differ.

Example 3 A Web site ed 1,000 of its members to determine its members’ favorite hobbies. The results are shown in the histogram. Identify any sampling errors and explain why the sample and display might be biased. The sample is a biased convenience sample. Members of a Web site probably enjoy computers more than other activities. The display is biased because the data used to create the display came from a biased sample.

Example 4 A.The sample is unbiased since it was mailed. B.The sample is biased because it is a voluntary response sample. C.The display is unbiased because it came from an unbiased sample. D.The sample is unbiased because it represents all pet owners. A pet store owner sent a mail survey to 200 of his customers to what kind of pet is most popular. The results are shown in the graph. Using this information, which of the following statements is true?

Example 5 Michael and Melissa both claim to be earning a C average— 70% to 79%—in their Latin class. One student is wrong. Which one? Explain how he or she is using a misleading statistic. Michael Melissa mean53.4% 71.9% median70%70%

Michael is wrong. He claimed to be earning a C average because his median was 70%. But his mean, or average, is much less than 70%.

Your Turn

Are you done copying ALL the notes and completing the example problems? Then work on Review W.S. (this is a review for Chapter 11 Test)