Problem 1: Skew, mean, and median

  1. Look at the distribution displayed in the histogram below. Is this a right skewed, left skewed, or symmetric distribution?
  2. Is the mean bigger than, smaller than, or equal to the median in this distribution?

Problem 2: Teacher salaries at SMART

Five teachers at SMART reported their annual salary in thousands of dollars. The salaries were recorded as follows: {38, 38, 51, 41, 38}

  1. Calculate the sample mean (average salary of the teachers in the sample) by hand. Show all your work.
  2. Calculate the sample standard deviation of salaries in the sample by hand. Show all your work.
  3. Are there any observations in the sample that are unusual in terms of the empirical rule? Explain.
  4. Would the mean or median do a better job of capturing what an “average” teacher at SMART makes? Explain your reasoning.