Review One Variable Statistics With Standard Deviation

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.

• 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.

• 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 are summarized in the histograms.

Is the standard deviation of number of toys donated greater for seniors or juniors?

• Juniors

• Seniors

The dot plots show the forearm lengths of 2 groups of 10 students. Select all the statements that must be true.

• The standard deviation of group A is equal to the standard deviation of group B.

• Group A has greater variability than group B.

• All of the people in group A have longer forearms than the people in group B

• Using only group A, the mean is equal to the median.

The dot plots show the amount of sugar in cereals advertised to adults and children.

Select all the statements that must be true.

• The mean and median amounts of sugar in adult and children cereals are the same.

• The median values of sugar in cereals for adults and children are about the same.

• The median value of the sugar in adult cereals will remain unchanged after a new cereal is introduced that contains 30 grams of sugar per serving.

• The new cereal with 30 grams of sugar per serving will affect the mean value for cereals for children more than the median value for cereals for children.

The residents of Townsville and Cityburg were surveyed about how much of a pizza they could finish in one sitting. 1 means a whole pizza and 0 means none of a pizza. The results are summarized in the histograms.

Is the standard deviation of the amount of pizza greater for Townsville or Cityburg?

• Townsville

• Cityburg