Pre-Algebra – Unit 11 Review – Statistics

What should I be able to do? Calculate measures of central tendency and choose the best measure to represent a data set (mean, median, mode)

Calculate the range and interquartile range of a data set and use these statistical measures to analyze the spread (variability) of the data

Create, analyze and interpret line plots and box-and-whisker plots

Recognize an outlier in a data set

Calculate the mean absolute deviation to measure the spread of a data set and explain its meaning

Recognize and identify unbiased and biased samples

Practice Problem Set – Use a separate sheet of paper to show all necessary work.

1. Determine whether the sample is biased or unbiased. Explain your response.

a. You want to find out what core class students in your grade like the most. You conduct a survey at one of the mathletes club meetings.

b. You want to estimate the number of people in a town who are in favor of the new curfew law. You survey every fifth person who enters the town’s post office.

2. This table shows the number of minutes Carol and Anna walked each day for 5 days. Which statement is true?

A. Anna’s mean for the number of minutes she walked is equal to Carol’s mean.

B. Carol’s mean for the number of minutes she walked is greater than Anna’s mean.

C. Anna’s median for the number of minutes she walked is greater than her mean.

D. Carol’s mean for the number of minutes she walked is equal to her median.

3. Use the box-and-whisker plot pictured to the right to complete a – e.

a. What is the median of the data? b. What is the lower quartile? c. What is the upper quartile? d. Calculate the range of the data. e. Calculate the interquartile range (IQR). f. What percentage of the data falls in between 4 to 12?

4. The Roslyn movie theater recorded the number of tickets sold daily for a popular movie during the month of May. The box-and-whisker plot shown represents the data for the number of tickets sold, in hundreds. What conclusion can be made based on the plot? A. The 50th percentile is 600. B. The mean number of tickets sold was 400. C. The IQR is 600. D. The number of tickets sold that ranged from 300 to 400 represents 25% of the data.

5. Create a box and whisker plot for the following set of test scores: 85, 97, 82, 65, 82, 91, 60, 98, 78

Lower Extreme:

Lower Quartile (Q1):

Median (Q2):

Upper Quartile (Q3):

Upper Extreme:

6. The dot plot below shows the number of pets owned by each student in a class of 24. a. Calculate the mean of the data. Round to the nearest tenth. b. Calculate the median of the data. c. Calculate the mode of the data. d. Which measure best represents the data set, the mean or median? Explain your response. 7. Calculate the mean absolute deviation for the set of data below that represents the ages of 8 children taking a beginner’s gymnastics class. Explain the meaning of the M.A.D that you calculated. Ages: 3, 4, 4, 4, 4, 5, 5, 5 8. Westover Middle School includes grades 6, 7 and 8. The middle school principal compares two sets of data from the school:

Data set A is the ages of the students. Data set B is the ages of the teachers.

Which set of data most likely has a greater mean absolute deviation, and why?

A. Data set B, because the mean of the students’ ages is less than the mean of the teachers’ ages. B. Data set B, because it is more likely that the range of the students’ ages is less than the range of the

teachers’ ages. C. Data set A, because there are more students than teachers in the school. D. Data set A, because it is more likely that the range of the students’ ages is greater than the range of

the teachers ages.