This dot plot shows the number of hours 20 sixth grade students slept on a Saturday night.
Which of the following statements is true?
A. Six students slept for at least 8 hours.
B. The mean amount of sleep was 6.25 hours.
C. More than half of the students slept 8 hours or more.
D. More students slept 6 hours than slept 8 hours.
E. The difference between the most hours of sleep and the least for these students was 2.5 hours.
Students responded to a survey. The survey asked students to report the amount of time they spent doing homework during a week, to the nearest hour. The histogram below displays the data.
Which of these statements must be true?
A. A total of 4 students participated in the survey.
B. Every student spent at least 1 hour doing homework.
C. More students spent less than 5 hours on homework than spent between 5 and 10 hours on homework.
D. The same number of students spent between 5 and 10 hours on homework as spent between 10 and 15 hours on homework.
Maya tracked the number of minutes she spent reading on each of 5 days last week.
| Day | Minutes Reading |
|---|---|
| Monday | 18 |
| Tuesday | 22 |
| Wednesday | 30 |
| Thursday | 25 |
| Friday | 25 |
What is the mean number of minutes Maya spent reading per day?
A. 12 minutes
B. 24 minutes
C. 25 minutes
D. 30 minutes
Tara recorded the number of laps she swam at swim practice on each day she went this month. The dot plot below shows her data.
What is the median number of laps Tara swam at practice?
A class collected data on the number of books each of 9 students read last month. The dot plot below shows their data.
Mai claims that the mean number of books read is greater than the median number of books read. Do you agree with Mai? Use the dot plot to support your answer.
A
A is true. Counting the dots at 8, 8.5, and 9 gives 3 + 2 + 1 = 6 students.
B is false: 6.25 is the midrange (the average of the largest value 9 and smallest value 4 plus a half-step adjustment), not the mean. The actual mean is about 6.7 hours.
C is false: Only 6 out of 20 students (30%) slept 8 hours or more, which is less than half.
D is false: The dot plot shows 2 dots above 6 and 3 dots above 8, so more students slept 8 hours than 6 hours.
E is false: The largest value is 9 and the smallest is 4, so the difference is 5 hours, not 2.5.
C
The bin heights are 8, 5, 3, and 1 (left to right). A is false: 4 is the number of bins, not the number of students; the total is 8 + 5 + 3 + 1 = 17 students. B is false: The first bin covers 0 to 5 hours, so some students may have spent less than 1 hour. C is true: The first bar (less than 5 hours) has 8 students, taller than the second bar (5–10 hours) with 5 students. D is false: The 5–10 bar has 5 students and the 10–15 bar has 3 students, so the counts are not equal.
B (24 minutes)
Sum the values: 18 + 22 + 30 + 25 + 25 = 120. Divide by the number of days: 120 ÷ 5 = 24. The mean is 24 minutes per day.
7 laps
List the data in order using the dot plot: 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9. There are 11 values, so the median is the 6th value. Counting in: the 6th value is 7. The median is 7 laps.
Yes, Mai is correct. The median is 2 books and the mean is 3 books, so the mean is greater than the median.
Sample reasoning: Listed in order, the 9 values are 1, 1, 1, 2, 2, 3, 5, 5, 7. The middle (5th) value is 2, so the median is 2. The mean is (1 + 1 + 1 + 2 + 2 + 3 + 5 + 5 + 7) ÷ 9 = 27 ÷ 9 = 3. Since 3 is greater than 2, Mai is correct. Other valid reasoning is accepted as long as it demonstrates understanding that the higher values at 5 and 7 pull the mean above the median.