2.12 Exercises  (Page 2/5)

An elementary school class ran 1 mile with a mean of 11 minutes and a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile with a mean of 9 minutes and a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile with a mean of 7 minutes and a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.

• a Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
• b Who is the fastest runner with respect to his or her class? Explain why.

In a survey of 20 year olds in China, Germany and America, people were asked the number of foreign countries they had visited in their lifetime. The following box plots display the results.

• a In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected.
• b Explain how it is possible that more Americans than Germans surveyed have been to over eight foreign countries.
• c Compare the three box plots. What do they imply about the foreign travel of twenty year old residents of the three countries when compared to each other?

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows:

• 3
• 8
• -1
• 2
• 0
• 5
• -3
• 1
• -1
• 6
• 5
• -2

• a What is the mean change score?
• b What is the standard deviation for this population?
• c What is the median change score?
• d Find the change score that is 2.2 standard deviations below the mean.

Three students were applying to the same graduate school. They came from schools with different grading systems. Which student had the best G.P.A. when compared to his school? Explain how you determined your answer.

Given the following box plot:

• a Which quarter has the smallest spread of data? What is that spread?
• b Which quarter has the largest spread of data? What is that spread?
• c Find the Inter Quartile Range (IQR).
• d Are there more data in the interval 5 - 10 or in the interval 10 - 13? How do you know this?
• e Which interval has the fewest data in it? How do you know this?
  • I 0-2
  • II 2-4
  • III 10-12
  • IV 12-13

Given the following box plot:

• a Think of an example (in words) where the data might fit into the above box plot. In 2-5 sentences, write down the example.
• b What does it mean to have the first and second quartiles so close together, while the second to fourth quartiles are far apart?

Santa Clara County, CA, has approximately 27,873 Japanese-Americans. Their ages are as follows. ( Source: West magazine )

• a Construct a histogram of the Japanese-American community in Santa Clara County, CA. The bars will not be the same width for this example. Why not?
• b What percent of the community is under age 35?
• c Which box plot most resembles the information above?