IMGD 2905 - Data Analysis for Game Development

Homework 1

Due: Wednesday, April 8th, 11:59pm

Homework will be turned in online (canvas) in written form, saved as a PDF.

Short answer

  1. What is the purpose of a measure of central tendency?

  2. Which of the following statements about the median is not true?

    1. It is less affected by extreme values than the mean.
    2. It is a measure of central tendency.
    3. It is equal to the range.
    4. It is equal to the mode in a bell-shaped, "normal" distribution.

  3. In a symmetric distribution:

    1. The median equals the mean
    2. The mean is less than the median
    3. The mean is greater than the median
    4. The median is less than the mode

  4. Which of the following measures of dispersion depend upon every value in the set of data?

    1. Range
    2. Standard deviation
    3. Both a and b
    4. Neither a nor b

  5. Consider the set of numbers: 9 1 1 10 7 11 5 8 2

    1. What is the mean?
    2. What is the median?
    3. What is the mode?
    4. What is the first quartile?
    5. What is the range?
    6. The data is: i) Right skewed, ii) Left skewed, iii) Symmetrical

  6. Consider the below histogram:

    1. What measure of central tendency would you use to describe it and why?
    2. What measure of variation would you use to describe it and why?

  7. Consider the below scatter plot (Figure 2):

    Which statement best describes the relationship between speed and traffic volume shown in the graph?

    1. As traffic volume increases, vehicle speed decreases.
    2. As traffic volume increases, vehicle speed increases.
    3. As traffic volume increases, vehicle speed increases at first, then decreases.
    4. As traffic volume increases, vehicle speed decreases at first, then increases.

Problems

Use a spreadsheet for the following problems.

  1. Download the data on New York's Winter Mean temperature.

    1. Create a scatter plot of the data. Be sure to label all axes.
    2. What conclusion can you reach about the relationship between time and mean temperature in New York?

  2. For professional sports, the cost of attending a professional game is often tracked by the Fan Cost Index: following data represents the cost of four tickets, 6 drinks, four hot dogs, two programs, to caps and the parking fee for one car at the arena for each professional team in a league. Here is the data for a professional eSports league.

    1. Compute the mean and median.
    2. Compute the quartiles.
    3. Compute the variance, standard deviation and range.
    4. Construct a box and whiskers plot and a histogram. Properly label all axes. Which might you prefer and why?
    5. Is the data skewed? How can you tell from your graphs in d?
    6. What would you use for a measure of central tendency? Why?
    7. Which teams have a particularly high cost index? How can you tell?
    8. Based on the results a-d, what conclusions can you reach concerning the Fan Cost Index for this league?

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