Show all of your work. Draw pictures. Make a point; justify it; illustrate it with an example.

A utility company is concerned about the ability of its vehicle operators to drive safely in its service region. It decides to sample a population of accidents in the 10461 zip code. One particular intersection comes to light. Analysts estimate that 2 accidents (“vehicular contacts”) per month occur at the intersection of Crosby and Westchester Avenues in the 10461 zip code in the Bronx.

Here is a summary of descriptive statistics.

mean median sd q1 q3 IQR skew kurtosis max min
2.976 3 1.7001 2 4 2 0.66627 6.6689 10 0

  1. What kind of data do we have here?

  2. Using quartiles as cumulative relative frequency, sketch a relative frequency and cumulative relative frequency plot. Label mean, median. Calculate and interpret the expected value of accidents and compare with the median accidents. Describe and interpret the IQR, standard deviation, skewness, and kurtosis.

  3. Draw a boxplot and label. Are there any outliers?

  4. How often are there are between 0 and 1 accidents (inclusive) or between 4 and 5 accidents? How often are there between 2 and 3 accidents (inclusive)? Explain.

  5. According to the Chebyshev rule what is the probability of finding accidents that are 2 standard deviations from the expected value? Does this check out with the data?

  6. Discuss the pros and cons of 3 different scale (width, volatility, dispersion) metrics for a distribution of data.