Activities

1. What is the range of the following set of data:  13, 25, 18, 11, 2, 3, 31, -12, 15, 19, 20, 31, 0 ?

2. What are the lower quartile, median, and upper quartile values for the set of data displayed below?

2, 5, 8, 11, 14, 19, 21, 21, 30, 33, 37, 40, 50

3. What is the interquartile range of the following values?

0, 2, 4, 6, 8, 9, 11

4. Ben bowled eight games over the weekend. His scores were 221, 187, 150, 200, 206, 211, 163, 98. What is the interquartile range of his data?

5. Caroline’s test scores throughout the year in her math class were: 81, 78, 83, 85, 77, 89, 86, 90, 82, 94, and 99. What are the values for the lower and upper quartile of her data?

6. Looking at the box and whisker plot below, determine the range, and interquartile range of the data. 

7. Each weekend, throughout the summer, Kevin goes for a hike along the Appalachian Trail. He wore a pedometer to track his distance. If the range of the lengths of Kevin’s hikes was 13 miles and his longest hike was 17 miles, what was his shortest hike?

8. Dan rode his bike across the state of Pennsylvania. It took him a total of 8 days to ride from Philadelphia to Pittsburgh. He kept track of how many miles he rode per day, the amounts were 81 miles, 65 miles, 61 miles, 27 miles, 45 miles, 63 miles, 25 miles and 60 miles. Determine the interquartile range of his data.

9. The high temperature over a span of 10 days in the summer included the following values in Fahrenheit:  77, 83, 91, 90, 87, 81, 81, 95, 81, and 90. What was the median temperature during that 10-day span?

10. The median age of a group of kids in an elementary school class is 10 years. If the lower quartile is 9 at least what percent of the students are 9 or 10 years old?

11. When Ida was bored one summer afternoon, she decided to count how many people were in each of the photo’s saved on her cell phone. The number of people in each of her 20 favorite photo’s were as follows: 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 6, 7, 8, 9, 11, 25. What are the range, upper and lower quartiles, and interquartile range of Ida’s data?

12. If the interquartile range of a set of numbers is 60 and the lower quartile value is 11 then…

1. Approximately 50% of the numbers are between ______ and ______
2. Approximately 25% of the numbers are less than _______
3. Approximately 25% of the numbers are greater than _______

13. A certain math teacher took a survey of her students who had jobs outside of school. She wanted to analyze their pay rate. Of the 25 students in her class, 11 had jobs. The pay rate for those 11 students in dollars per hour was as follows:  5, 6.25, 6.25, 6.25, 6.25, 6.75, 7, 7.50, 9, 12, and 15. Their teacher was able to identify that approximately 50% of the students earned between what two values?

14. What are the upper and lower quartile values of the following set of numbers?

15. The height of various children, in inches, is listed below. The tallest 25% of children are approximately taller than what height?

31, 27, 41, 42, 28, 33, 50, 47, 41, 39, 46, and 40

16. Describe, in your own words, the definitions of the following terms:
    1. Range
    2. Lower Quartile
    3. Median
    4. Upper Quartile
    5. Interquartile Range

17. Thomas loves playing old arcade games. If the median score of a certain game was 210,000 points and his range was 100,000 points, can you determine his high score?

18. Predict the median and range and interquartile range of the age of the students in your classroom. Do not use any actual data, only your best estimation.

19. Create a list of 7 numbers that have the following values: range = 8, lower quartile = 2, upper quartile = 9.

20. If the middle 50% of the students in a math class had a grade between 81% and 87% and the median grade was an 84% you can be certain that what percent of the class had a grade between 84% and 87% inclusive?

21. A school wide study was trying to determine how many hours per night students spend doing schoolwork. The study found that the minimum value was 0 hours and the lower quartile value was 0.5 hours. Additionally, they determined that the range was 5 and the interquartile range was 2.5. Determine how many hours the 25% of students who studied the most spent doing schoolwork each night.

22. Determine the interquartile range for the following set of data:  0, 0, 0, 0, 0, 0, 1, 15.

23. Determine the interquartile range of the numbers from 0 to 99 without writing them down.

24. The interquartile range of a set of test scores is 28 points. If the upper quartile value is 24 points less than twice the lower quartile. What is the upper quartile value?

25. Evan surveyed 25 classmates to determine how many text messages they sent per day. He analyzed the data and determined that:

1. The median value was 100 text messages
2. The lower quartile was 50 text messages
3. The upper quartile was 200 text messages

What is the maximum number of students who could have sent 100 text messages per day?

Answer Key/Rubric

1. 43

2. Lower Quartile: 9.5, Median: 21, Upper Quartile: 35

3. 7

4. 52

5. Lower Quartile: 81, Upper Quartile: 90

6. Range: 31, Interquartile Range: 16

7. 4 miles

8. 28 miles

9. 85 degrees Fahrenheit

10. 25%

11. Range: 25, Upper Quartile: 6.5, Lower Quartile: 1, Interquartile Range: 5.5

12. 
    
    1. Approximately 50% of the numbers are between 11 and 71
    2. Approximately 25% of the numbers are less than 11
    3. Approximately 25% of the numbers are greater than 71

13. $6.25 and $9.00

14. Upper Quartile: , Lower Quartile:

15. 44 inches

16. Various wording…
    1. Range – The difference between the maximum value and the minimum value
    2. Lower Quartile – The middle value of the lower half of the data
    3. Median – The middle value of the data
    4. Upper Quartile – The middle value of the upper half of the data
    5. Interquartile Range – The difference between the upper and lower quartile values

17. There is not enough information to determine this number

18. Various answers depending on grade. Interquartile range should probably 1 or less

19. Various answers could be 2, 2, 2, 8, 8, 9, 10

20. 25%

21. 3 to 5 hours

22. 0.5

23. 50

24. 80

25. 13 students