Measures of Central Tendency

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 situation;

2. 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. Mean

3. 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. Median

4. 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. Mode

5. 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 (Statistical) Range

6. If Amy wants to have a test average of 90, what must she make on her 6th 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 6th and last test! • Amy cannot make an average of 90 unless there is extra credit given on her last test! Example Note: Some form of this question has appeared on several TAKS tests in the past!

7. 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 Practice Problem #1 Check Answer

8. 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 Practice Problem #2 Check Answer

9. 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 Practice Problem #3 Check Answer

10. 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 Practice Problem #4 Check Answer

11. 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 Practice Problem #5 Check Answer

12. 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 Practice Problem #6 Check Answer

13. 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 Practice Problem #7 Check Answer

14. 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 Practice Problem #8 Check Answer

15. 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. Practice Problem #9 Check Answer

16. 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 Practice Problem #10 Check Answer

17. Now, log in to Study Island at www.studyisland.com • Complete the assignment titled “Measures of Central Tendency” – work 10 problems in test mode. • The Study Island assignment will account for half of today’s grade, so you need to do it! (There is a poster on the back wall with Study Island instructions, in case you forgot how to log in & access the assignment.) Study Island End Show

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

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

20. 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 Answer to Problem #3 Back

21. 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 Answer to Problem #4 Back

22. 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) Answer to Problem #5 Back

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

24. 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. Answer to Problem #7 Back

25. 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) Answer to Problem #8 Back

26. 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. Answer to Problem #9 Back

27. 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. Answer to Problem #10 Back