Exploring Data: Measures of Central Tendency, Quartiles, Percentiles & Box Plots Name:_____________________ Date:______________________ Box-and-whiskers plot Five-number summary Index Interquartile range Mean Measures of center Median Mode Outlier Algorithm Quartiles Sigma Notation Spread 1. Be able to define, explain, and supply examples 2. Give a data set with 6 numbers in it satisfying each constraint. a. The mean is 50 and the median is 50. b. The mean is 50 and the median is 60. c. The mean is 50, the median is 100, and the mode is 75. (Hint: Numbers can be positive or negative.)

5. The chart at the right gives information about the height of the varsity basketball at team Hillsboro High School. a. How many members does the team have? b. Find the mean height. c. Find the median height. d. Which number, the mean or the median, best describes the typical height of a member of the team? Why? 4. x i equals the normal precipitation in inches in the ith month of the calendar year in Memphis, TN. a. Write an expression using  -notation to represent the yearly precipitation in Memphis, TN. b. Evaluate your expression in part a. c. Consider the expression. What does this expression represent? d. Evaluate the expression. 3. Consider the set {x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8 }. a. Which of these expressions represents the sum of the elements of the set? b. What expression represents the mean of the elements of the set? c. From the given information, can the median of the set be determined? If so, determine it. If not, explain why it cannot be determined.

7. Use the following scores of a mathematics class on the midyear exam a. Find Q1, Q3, and the median. b. Find the percentile rank of 89. c. What test score is at the 20th percentile? d. Use the 1.5 X IQR criterion to determine if there are any outliers. 8. The box plots below describe the ratings of the top 15 rated television shows in 1984 and in 1994–95. a.Estimate the range of ratings of the top 15 rated television programs in b. Estimate the ratings of the 10th highest rated program in 1994–95. c.The highest rated program in 1995 had the same rating as the ? highest rated program in d.Do these data support the statement that the amount of viewing of television programs decreased between 1984 and1994–95? Explain your answer. 6. Use the data given for Example 3 on page 23 a. Find the median of the numbers above the median. b. Find the median of the numbers below the median.

9. The stemplot at the right gives the prices, rounded to the nearest dollar, of the 30 stocks in the Dow Jones Industrials on January 2, 1996, and December 31, a. Find the five-number summaries for each date. b. Find any outliers using the 1.5 X IQR criterion c.The only two stocks which posted a decrease in price for 1996 were McDonald’s, which started at 46 and dropped to 45, and Bethlehem Steel. If Bethlehem Steel stock opened the year at 14, what was its change for the year? d. The Dow Jones Industrials is one of many indices used to gauge the entire stock market. Based on the above data, do you think the stock market increased or decreased for the 1996 year? Justify your answer. e. Draw two box plots to illustrate the data

Exploring Data: Histograms Name:_____________________ Date:______________________

Exploring Data: Choosing a Good Display Name:_____________________ Date:______________________

Exploring Data: Variance & Standard Deviation Name:_____________________ Date:______________________