1. Measures of Central Tendency The student uses statistical procedures to describe data. The student is expected to use variability (range, including interquartile range (IQR)) and select the appropriate measure of central tendency to describe a set of data and justify the choice for a particular situationdata Retrieved from: http://www.cocisd.org/ and modified as needed.http://www.cocisd.org/

2. Mean Mean: The mean of a set of data is the sum of the data divided by the number of pieces of data. It is the same thing as the average. Amy’s test grades in math class are 88, 93, 90, 76, and 88. To calculate her mean, or average, test grade, find the sum of all the grades, then divide that answer by 5, since there are 5 grades. (88+93+90+76+88) ÷ 5 = 87 Amy’s mean, or average, test grade is 87.

3. Median Median: The median is the middle number when the data are arranged in numerical order. To find Amy’s median, or middle, test grade, arrange the grades in order from least to greatest and find the middle grade. 76, 88, 88, 90, 93 Amy’s median test grade is 88. NOTE: If she had an even number of grades, there would not be a middle number. In that case, you have to find the average of the two middle numbers.

4. Mode Mode: The mode of a set of data is the number(s) or item(s) that appear most often. To find the mode of Amy’s test grades, find the test grade that appeared most often: 88. NOTE: If no score had appeared any more often than the others, there would have been no mode. If two or more scores had appeared twice, there would have been two modes.

5. (Statistical) Range Range: The range is the difference between the greatest number and the least number in a set of data. To find the range of Amy’s test grades, find the difference between the highest and the lowest grade: 93 – 76 = 17

6. Example If Amy wants to have a test average of 90, what must she make on her 6 th and final test? To figure this out, follow these steps: In order to have an average of 90 on six tests, her total score on all six tests combined must be equal to 540. (90 × 6) Add her first 5 tests together to get her total score to date. Then subtract this answer from 540. (540 – 435 = 105) Amy needs a 105 on her 6 th and last test! Amy cannot make an average of 90 unless there is extra credit given on her last test! This one is handy! You’ll use it again in life!

7. Practice Problem #1 The tenth grade class at Jones High School conducted a survey to pick its favorite song to play at the awards banquet. Which of the following measures of central tendency of the collected data is the BEST to use to select the favorite song? A. Mean B. Median C. Mode D. Range

8. Practice Problem #2 Marisa made the following test scores in her science class. 99, 91, 98, 94, 93, 99, 92. Which of the following measures of central tendency is the BEST to use to determine her final grade in her science class? A. Mean B. Median C. Mode D. Range

9. Practice Problem #3 The scatterplot indicates the yearly snowfall, in inches, in Chillyville for the years 2000 to 2005. What is the mean snowfall in Chillyville for the years shown? A. 45 inches B. 37 inches C. 35 inches D. 25 inches

10. Practice Problem #4 The table shows the temperatures that Mark recorded each day at 4:00 p.m. last week. What was the average temperature last week? A. 39° F B. 49° F C. 50° F D. 55° F

11. Practice Problem #5 The Greater Texas Real Estate Association is advertising new homes in a subdivision. The prices of the homes range from $100,000 to $175,000. There are 50 homes in the new subdivision. What statistical measure describes the price of a home that is more expensive than half of the homes in the subdivision and less expensive than the other half of the homes in the subdivision? A Mean B Median C Mode D Range

12. Practice Problem #6 Nigel and his class created a bar graph showing everyone's favorite color. The data collected is shown below. Based on the graph, which measure of data is represented by the color blue? A. Range B. Mean C. Median D. Mode

13. Practice Problem #7 Last Friday a used-car dealer had cars for sale for $600, $690, $695, $710, $725, $750, $850, $995, $995, $995, and $1495. Select the most effective measure to use to convince potential customers that the dealer’s prices are very low. A. Mean B. Median C. Mode D. Range

14. Practice Problem #8 Millie entered her dog in a dog show. Her dog got a score of 64. Which measure of data can Millie use to determine whether her dog’s score was in the top half of all scores at the show? A. Median B. Mode C. Mean D. Range

15. Practice Problem #9 Given the set of data {20, 15, 10, 20, 15, 10, 20, 20, 50}, which statement best interprets the data? A. Only the mean is 20. B. The range of the set of data is 20. C. The mean, median, and mode are all 20. D. The mode and median are not the same.

16. Practice Problem #10 The table below shows the number of pages in novels that Chloe read for pleasure each month during the school year. If Chloe read only 125 pages during the month of May, which measure of data changed the most? A. The mean B. The median C. The mode D. All measures were equally affected

17. Extra HELP!!!! http://www.regentsprep.org/regents/math/al gebra/ad2/pmeasure.htm http://www.regentsprep.org/regents/math/al gebra/ad2/pmeasure.htm www.khanacademy.org  http://www.khanacademy.org/math/probability/descrip tive-statistics/central_tendency/v/statistics-intro-- mean--median-and-mode (central tendency) http://www.khanacademy.org/math/probability/descrip tive-statistics/central_tendency/v/statistics-intro-- mean--median-and-mode  http://www.khanacademy.org/math/probability/descrip tive-statistics/Box-and-whisker%20plots/v/reading- box-and-whisker-plots (box and whisker) http://www.khanacademy.org/math/probability/descrip tive-statistics/Box-and-whisker%20plots/v/reading- box-and-whisker-plots www.purplemath.com  http://www.purplemath.com/modules/meanmode.htm http://www.purplemath.com/modules/meanmode.htm

18. Answer to Problem #1 Correct Answer: C The favorite song would be the song that most of the students chose. Mode = Most

19. Answer to Problem #2 Correct Answer: A The final grade is calculated by finding the average of all the grades. Mean = Average

20. Answer to Problem #3 Correct Answer: C Add the amount of snowfall for each year; divide the sum by the number of years. (55+30+35+35+15+40) ÷ 6 = 35

21. Answer to Problem #4 Correct Answer: D Add the temperatures for each day; divide by the number of days. (Round the answer to the nearest whole number.) (86+50+50+49+47+49+53) ÷ 7 = 55

22. Answer to Problem #5 Correct Answer: B The statistical measure that is more expensive than half, and less expensive than half, would be the number exactly in the middle. Median = Middle (when data is arranged in order)

23. Answer to Problem #6 Correct Answer: D Blue is the color chosen most often. Mode = Most

24. Answer to Problem #7 Correct Answer: B Find the measure that provides the lowest number: Mean (average) = 864 Median (middle #) = 750 Mode (most often) = 995 Range (the difference between the highest & lowest amount) is not applicable for this problem.

25. Answer to Problem #8 Correct Answer: A Since the median is the middle number, it can be used to determine if a score is in the top half or lower half. Median = Middle (when the data are arranged in order)

26. Answer to Problem #9 Correct Answer: C The mean (average) = 20 The range = 50 – 10 = 40 The median (middle #) = 20 The mode (most) = 20 Therefore, the mean, median, and the mode are all equal to 20.

27. Answer to Problem #10 Correct Answer: A Current mean = 383 Mean, including 125 pages in May = 354, a decrease of 29 pages Current median (the average of the 2 middle #s) = 382.5 Median, including 125 pages in May = 380; a decrease of only 2.5 pages There is no mode; no number was repeated more often than the others.