Unit 1 IM Test Review

The two box plots summarize the number of hours spent in the weight room for all the players on the football team for two different high schools. Which of the statements must be true about the distribution of data represented in the boxplots?

• Players at school 1 typically spent more time in the weight room than players at school 2.

• The middle half of the data for school 1 has more variability than the middle half of the data for school 2.

• The median hours spent in the weight room for school 1 is less than the median for school 2 and the interquartile ranges for both schools are equal.

• The total number of hours spent in the weight room for players at school 2 is greater than the total number of hours for players at school 1.

The dot plots show 9 scores on a 10-question trivia game for two students. Select all the statements that must be true. (hint, there are 3)

• Noah’s scores have greater variability than Jada’s scores.

• The standard deviation of Noah’s scores is equal to the standard deviation of Jada’s scores.

• The mean of Noah’s scores is greater than the mean of Jada’s scores.

• Noah scored better than Jada on every assignment.

• Using only Noah’s scores, the mean is equal to the median.

The dot plots show the salaries for the employees at two small companies before a new company head is hired at each company. Select all the statements that must be true. (hint, there are 3)

• The mean and median values of salaries shown in the dot plot for company 2 are the same.

• The standard deviation of salaries shown in the dot plot for company 2 is greater than the standard deviation of salaries at company 1.

• The median values of salaries shown in the dot plots for the two companies are about the same.

• The median value of salaries at company 1 will remain unchanged after a company head is hired to have a salary of 500 thousand dollars.

• The new company head with a salary of 500 thousand dollars will affect the mean value for salaries at company 2 more than the median value for salaries at company 2

A school has a toy drive for a holiday in which students bring in toys to be donated to charity. The number of toys donated by juniors and seniors is summarized in the histograms. Is the standard deviation of the number of toys donated greater for seniors or juniors?

• Seniors

• Juniors

The chess club at a school has 15 members. The number of games won in tournament play this season by each member is listed with a box plot displaying the data.

                                    

What measure of center is most appropriate to use to describe a typical value for the data in this distribution?

• Mean, since the data appears to not have any outliers.

• Median, since the data appears to be skewed to the right.

The chess club at a school has 15 members. The number of games won in tournament play this season by each member is listed with a box plot displaying the data.

                                    

What measure is most appropriate for describing variability in this data distribution?

• Interquartile range

• Standard deviation

Diego arranges the students in his math class from shortest to tallest and measures the height in inches of each student in the class. The heights of the 22 shortest students and the tallest 8 students are summarized in the histogram.

Which is greater, the mean or the median? 

• The mean because the distribution is skewed to the right.

• The median because the distribution is symmetric.

The mean vitamin C level for 20 dogs was 7.6 milligrams per liter, with a standard deviation of 2.1 milligrams per liter.

One dog’s vitamin C level was not in the normal range. It was 0.9 milligrams per liter, which is a very low level of vitamin C.

1. If the value 0.9 is eliminated from the data set, does the mean increase or decrease?

• The mean will increase because 0.9 milligrams per liter is below the mean of 7.6 milligrams per liter.

• The mean will decrease because 0.9 milligrams per liter is above the mean of 7.6 milligrams per liter.

The mean vitamin C level for 20 dogs was 7.6 milligrams per liter, with a standard deviation of 2.1 milligrams per liter.

One dog’s vitamin C level was not in the normal range. It was 0.9 milligrams per liter, which is a very low level of vitamin C.

1. If the value 0.9 is eliminated from the data set, does the standard deviation increase or decrease?

• The standard deviation will increase because 0.9 milligrams per liter is very close to the mean, so the new data set will be less concentrated around the center when that value is removed.

• The standard deviation will decrease because 0.9 milligrams per liter is very far from the mean, so the new data set will be more concentrated around the center when that value is removed.