Warm up case study 1: Hospital weights

  1. A doctor collects the weights of ten cancer patients in pounds and writes them as follows: {156, 177, 131, 145, 199, 200, 171, 161, 120, 118}. What is the mean of these data? What is the standard deviation of these data?
  2. Suppose the scale in the hospital was inaccurate and added ten pounds to everyone’s weight. Then each observation would be ten less than recorded. Using the true weights that are ten less, what is the new mean of the data? What is the new standard deviation? Try to think of a rule for how this change effected the mean and standard deviation.

Warm up case study 2: Stocks and portfolios

  1. You own five stocks and the price (in dollars) of the stocks is recorded as follows: {30, 20, 10, 10, 40}. What is the mean price of these stocks? What is the standard deviation of the price of these stocks.
  2. If the price of each of the stocks increased by 10% what would the new mean of stock prices? What would be the new standard deviation of stock prices?

Case study 1: Calculating the curve

For this case study we will be using the combined midterm data for both of the stats classes. Our main goal is to generate a curved score for each student in the class such that the mean score for students across both classes is an 82.

  1. Using the methods discussed in class create a new variable named PercentScore that transforms the raw point score into a percentage.
  2. Plot the distribution of PercentScore using a histogram. What seems to be the center of the distribution?
  3. Calculate the mean and standard deviation of PercentScore.
  4. When curving an exam using a ‘straight curve’ a certain constant percentage is added to each person’s score so that the desired increase in the mean is achieved. Suppose Bradshaw wants to increase the mean to an 82. How much should we add to each score to achieve this increase?
  5. Create a new variable named CurvedScore that is equal to PercentScore + curve. Where curve is the amount we decided to add to each observation.
  6. Plot the distribution of CurvedScore. What do you notice when comparing the distribution of PercentScore to CurvedScore?
  7. Calculate the mean and standard deviation of CurvedScore. Is the mean of CurvedScore = 82?
  8. Challenge: Transform CurvedScore back into a raw points variable so that Bradshaw can enter the curved score in the grade book.

Case Study 2: January 2015 high temperatures in Denver

The TempData data set contains daily high temperatures in Denver from January 2015 in degrees celcius.

  1. Plot a histogram of the daily high temperatures. What is the shape of the distibution.
  2. Calculate the mean an standard deviation of the daily high temperatures.
  3. The formula to convert degrees farenheit to degrees celcius is given by C = (F-32) x (5/9) where F is the temperature in degrees we would like to convert. Create a new variable CelcTmP that gives us the high temperature in Celcius for all days in January.
  4. Calculate the mean and standard deviation of the CelcTmp variable. How do these new values relate to the mean and standard deviation of the Farenheit variable?