Statistic

What is the Q1, Q2, and Q3 of the following data set?

4, 5, 6, 8, 9, 10, 11

• Q1: 4

  Q2: 8

  Q3: 11

• Q1: 5

  Q2: 8

  Q3: 10

• Q1: 4

  Q2: 5

  Q3: 6

Select all the true statements.

• Given a box plot, it is always possible to calculate the mean of the data.

• Given a box plot, it is always possible to calculate the median of the data.

• Given a box plot, it is always possible to construct a corresponding dot plot.

• Given a dot plot, it is always possible to construct a corresponding box plot.

• Given a histogram, it is always possible to construct a corresponding box plot.

Here’s a dot plot of a data set. Which statement is true about the mean of the data set?

• The mean is less than 5.

• The mean is equal to 5.

• The mean is greater than 5.

• There is not enough information to determine the mean.

The air quality was tested in many office buildings in two cities. The results of the testing is shown in these box plots. A level of less than 50 parts per million is considered healthy. A level of 50 or more parts per million is considered unhealthy.

Select all the statements that must be true.

• The lowest recorded measurement was in city Q.

• All buildings tested in city P are in the healthy range.

• The mean for city P is greater than the mean for city Q.

• The range for city Q is greater than the range for city P.

• The median for city P is greater than the median for city Q.

This box plot displays information about the number of text messages some students sent one day. What is the median number of texts sent by students?

• 10

• 20

• 14

• 26

This box plot displays information about the number of text messages some students sent one day. What is the IQR (interquartile range)?

• 10

• 20

• 14

• 26

This box plot displays information about the number of text messages some students sent one day. Is this data set symmetric? Explain how you know.

• Yes. It is equal on both sides of the median.

• Yes. The whiskers are the same width.

• No. The bottom quartile is much wider than the top one.

• No. The top quartile is much wider than the bottom quartile.

Mai drew two box plots to show the scores for two groups of friends who went bowling. Which group shows greater variability?

• The first group shows greater variability because it has a wider range (120) and a wider IQR (50).

• The second group shows greater variability because there is a longer bottom whisker.

• The groups have about the same variability, but the first group had higher scores overall.

Ten students each attempted 10 free throws. This list shows how many free throws each student made. What is the median number of free throws made?

• 6.5

• 65

• 6

• 7

Ten students each attempted 10 free throws. This list shows how many free throws each student made. What is the IQR (interquartile range)?

• 8

• 5

• 3

• 13