Statistics Homework


Name: ______________________________________

Problems: 10 points each.

  1. Draw a tree diagram for the situation in which:
    For your first course, you can have soup or a salad.
    For your second course, you can have beef, chicken, or pasta.
    For your third course, you can have cake or ice cream.
    What is the number of total possible dinners you can have?






  2. For your trip home from SJC, you first can choose to get to Grand Army Plaza by bus, by subway, or by cab.
    From there, you get either a bus or a subway.
    You get out at your stop, and then you can either walk home or rent a CitiBike.
    Draw a tree diagram for this situation.
    What are the total number of routes home open to you?






  3. Draw a Venn diagram for these three sets:
    "States in New England", "States beginning with M", "States bordering Canada".
    Use state abbreviations (e.g., "NY") to fill in the members of each set.
    What is the intersection of the three sets?
    (You can easily find a list of states, a map, and a list of New England states online.)







  4. We have the following set of data for ages of students in a class: 23, 43, 19, 19, 62, 18, 19, 27, 29, 17, 38.
    What is the mean age? What is the median age? What is the mode?






  5. Draw a histogram for income distribution at a company if we have employees making: $30,000; $32,000; $36,000; $44,000; $48,000; $52,000; $53,000; $57,000; $59,000; $61,000; $63,000; $72,000; $78,000; and $84,000.








Multiple Choice: 5 points each.

  1. Imagine a multiple choice test with five questions, each with four answers.
    What are the odds that two students guessing randomly will turn in the exact same test?
    (By same test, I mean each answer is identical.)
    1. 1 in 5
    2. 1 in 4
    3. 1 in 1024
    4. 1 in a million
  2. If you have a fair, 12-sided die, what are the chances of rolling a seven?
    1. 1 in 7
    2. 1 in 12
    3. 1 in 6
    4. No one can say
  3. Let's say the odds of someone in your building winning the lottery are one in a million.
    Your neighbor wins the lottery today.
    What are your odds of winning it tomorrow?
    1. One in a trillion (1/1000000 * 1/1000000)
    2. Very good: your building is on a lucky streak.
    3. Very bad: your building won't be "due" again for a while.
    4. One in a million
  4. Your friend is usually only sick once a year.
    She is sick today. What are the odds that she will be sick tomorrow?
    1. 1 in 365
    2. 1 in 2
    3. Can't say: the events are not independent.
    4. 1 in 7
  5. In a spa, a person can choose Swedish or Thai massage,
    followed by Russian sauna or Finnish sauna,
    followed by a salt scrub or a facial or a manicure or a pedicure.
    How many possible visit plans are there?
    1. 3
    2. 8
    3. 16
    4. 32
  6. If a distribution has a "fat tail," that means:
    1. A few values dominate the population.
    2. There is a fat chance of finding out anything about it.
    3. The mean, median and mode will all be the same.
    4. It looks like the standard bell curve.
  7. When we want to know about a population but it is too big, we
    1. give up.
    2. sample.
    3. guess.
    4. distribute.
  8. Statistics that tell us about the spread of a distribution include:
    1. the mean, the mode, and the median.
    2. probability, set theory, and expectations.
    3. skewness, kertosis, and gamma.
    4. the variance, the standard deviation, and the range.
  9. If we want to create a sample to gain information about a population, the best way to do so is:
    1. put in exactly the proportion of members of the population into our sample as exist in the general population.
    2. ask for as many volunteers as possible to fill in a questionnaire.
    3. put up a survey on the Internet and see who answers it.
    4. randomly pick members of the population.
  10. If we have a population with some very extreme values, the best measure of its average is:
    1. the mean.
    2. the median.
    3. the mode.
    4. the variance.