Reviewing Data Sets

Reviewing Data Sets

Create a Data Set

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Create a Data Set

  1. Create a student height data set consisting of 20 values that meets the following criteria:
    • The mean height is 64 inches.
    • The median height is 62 inches.
    • The range is 11 inches.
  2. List the set of data and show how it results in the given measures.
  3. Can you create another data set that results in the given criteria but does not include the data value of 64 inches?

Bouncing Ball Experiment

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Bouncing Ball Experiment

Part 1

In this unit you analyzed data to decide what is typical. Often your conclusion answered a question, such as “How tall is a sixth grade student?” In an experiment a question is also asked, but the question usually takes the form of “What will happen if ...,” rather than asking about the current status of something (height, for example). Experiments also often involve collecting data to answer the question. A hypothesis is the experimenter’s prediction about what he or she thinks the answer to the experimental question is.

Conduct an experiment to answer the following question: “How high will a ball bounce if it is dropped from a height of 3 feet?”

  1. Write your hypothesis about what will happen. Will the ball bounce half of its drop height? More? Less?
  2. Tape a yardstick or tape measure to a wall. Drop a ball from 3 feet and record how high it bounces in inches (or fractions of an inch).
  3. Repeat the experiment 20 times.
  4. Make a line plot for the data.

Part 2

  1. Calculate the mean, median and range.

  2. Why do you think there was a range of data?

  3. Decide the answer to your question. Was your hypothesis correct?

  4. Justify your conclusion using the line plot and measures as evidence.

  5. Do you think you need more data? Why or why not?

Adding New Data to a Data Set

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Adding New Data to a Data Set

Part 1

Use this data set to answer the questions that follow.
{ 1, 1, 2, 2, 2, 2, 3, 3, 4, 5 }

  1. Determine the mean and median.

  2. Identify a real-life situation that this data set could realistically represent.

  3. What happens to the mean if a new number is added to the data set—for example:

    • What if 2 is added?

    • What if 0 is added?

    • What if 8 is added?

  4. What happens to the mean if the numbers 2 and 3 are added to the given data set? Why does this result occur?

Part 2

  1. Find two numbers, that when added to the given data set, do not change the mean. How did you choose the two numbers?
  2. Find three numbers, that when added to the given data set, do not change the mean. How did you choose the three numbers?
  3. What happens to the mean if the number 30 is added to the given data set? How well does the mean represent the data set? Can you find another statistical measure that better represents the data set?
  4. Find two numbers, that when added to the given data set, change the mean but do not change the median. How did you choose the two numbers?
  5. Find two numbers, that when added to the given data set, change the median but do not change the mean. How did you choose the two numbers?

Bowling Scores

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Bowling Scores

In this problem you will create bowling score data sets that meet different criteria. Note that bowling scores may be any whole number in the range 0–300 (most people score in the range 100–200). Create a new data set for each question.

  1. Create a data set of seven scores in which the data meet the following criteria: The mean and the median are the same but the mode is different.
    • Mean of the set of scores
    • Median of the set of scores
    • Mode of the set of scores
  2. Create a data set of seven scores in which the data meet the following criteria: The mode is lower than the median but the mean is higher than the median.
    • Mean of the set of scores
    • Median of the set of scores
    • Mode of the set of scores
  3. Create a data set of eight different scores (that is, none of the scores can be the same) in which the data meet the following criterion: When the eighth score is added to the set, it does not change the mean.
    • Mean of the first seven scores
    • Mean of all eight scores

Mean Number of Fillings

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Mean Number of Fillings

  1. Ten people sit in a dentist’s waiting room. The mean number of fillings they have in their mouths is 4. Yet none of the 10 people actually have 4 fillings. Explain how this situation is possible.
  2. These are all true statements. Explain why each one must be true.
    • At least one person has more than 4 fillings and at least one has fewer than 4 fillings.
    • No person has more than 40 fillings.
    • From 0–9 people could have 0 fillings.
    • At least 2 people must have fewer than the mean number of 4 fillings.
    • It is not possible that all 10 people have an equal number of fillings.

Forestland

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Forestland

The top box plot shows the percentage of the land in 20 European countries that is forestland.

  • Read each statement below. Based on the top box plot, decide whether each statement must be true, may be true, or cannot be true. Then justify your answer mathematically.
    • In most of the 20 countries, between 35% and 76% of the land is forestland.
    • In at least one country, exactly 28% of the land is forestland.
    • The mean of the data for these countries is 28%.
  • If the box plot looked like the bottom one, could there be a data set for which the median and mean are both 28%? Explain why or why not this would be possible.

What's My Data?

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What's My Data?

  1. Create a data set for the histogram. Explain how you chose your data set.
  2. How many data points are there? Explain how you know.
  3. What bin is the median in? How do you know?
  4. Adjust your data set so that there is an outlier as far from the other data as possible.
  5. Adjust your data set so that the range is as narrow as possible.
  6. Adjust your data set so that the mode is in the 15 to 19 bin.

What's My Data 2?

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What's My Data 2?

This box and whisker plot represents the quiz scores of 13 students in Mr. Beel’s science class.

  1. Find the five number summary for the data shown in the box plot.
    • Lower extreme
    • Lower quartile
    • Median
    • Upper quartile
    • Upper extreme
  2. What do these numbers tell you about the data?
  3. What is the interquartile range (IQR)? What does it tell you about the data?
  4. Create a set of 13 data values for the box plot. Explain how you chose your data set.
  5. Adjust your data set so that the values are clustered around the extreme values and the median.
  6. Adjust your data set so that the values are clustered around the lower and upper quartiles.

Compare Graphs

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Compare Graphs

  1. Make a box plot and a histogram that represent the data in the line plot.
  2. Which of the three graphs represents the data best? Why do you think so?

Random Numbers

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Random Numbers

  1. Use a random number generator to generate 100 random numbers from 1 to 50, and then order the data. Random number generators can be found on the internet, in spreadsheet software, and on some calculators.
  2. Make a histogram with a bin width of 5 based on the data.
  3. What does your histogram look like? Do the data values appear to be random? Why or why not?
  4. Repeat steps 1 and 2, this time using 200 random numbers, and compare the results.
  5. Does using more data confirm or change your conclusion from question 3?

No Telephone?

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No Telephone?

For each one of the 50 states, the U.S. Census Bureau provides information about the percentage of households without a telephone. The percentage varies from state to state: In some states it is higher, while in others it is lower.

The box plot summarizes state telephone data for two different years—1960 and 1990.

  • What do the box plots tell us about how telephone ownership in the 50 states changed from 1960 to 1990? Write an explanation. Provide as much specific information as you can.

Who Is Taller?

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Who is Taller?

To find out who is taller, the boys or the girls in your class, you need to separate the data set of student heights you collected in Lesson 2 into two data sets: one for boys and one for girls.

  1. Make a line plot for each set of data. In order to compare the two plots, make the range and intervals of the horizontal line the same for both plots. Position one plot directly above the other.

  2. Calculate the mean, median, mode, and range for each plot.

  3. Decide which group of students is taller, and justify your answer using the measures you calculated.

  4. How does each line plot compare to the class line plot for all of the students?