Lab 4

Shape, dispersion, and central tendency

Instructions

Complete the following assignment using a word processing program and the R Project for Statistical Computing. When you are finished, upload your work (both the .pdf and the R file) to the dropbox on Canvas.

Objectives

  • Calculate standard deviation by hand
  • Differentiate between sample and population standard deviation when appropriate
  • Compute and interpret measures of distribution shape, namely kurtosis and skewness
  • Confirm or refute a claim based on measures of distribution shape, dispersion, and central tendency
  • Gain more experience using R for descriptive statistics

Part 1

Calculate the mean, median, and population standard deviation of the following two data sets by hand. You may use a calculator, but show your work and embed it in the document you turn in (a picture would be fine). Before you begin, make a prediction about which dataset has the greater standard deviation.

Dataset A: 14, 23, 13, 15, 15

Dataset B: 21, 21, 30, 21, 27

  1. Prediction and reasoning (1 pt.):

  2. Descriptive statistics for Dataset A

    1. Mean (0.5 pt.):
    2. Median (0.5 pt.):
    3. Standard deviation (2 pts.):

  3. Descriptive statistics for Dataset B

    1. Mean (0.5 pt.):
    2. Median (0.5 pt.):
    3. Standard deviation (2 pts.):

Part 2

You have been given the task of analyzing test scores from the Eau Claire School District. Below is a sample of standardized test scores from juniors at Eau Claire North and Eau Claire Memorial High School. Traditionally Eau Claire Memorial has had higher test scores, leading some to question the teaching methods of those at Eau Claire North. Public perception has led some to suggest that new teachers be sought at Eau Claire North.

You are to examine both sets of test scores and calculate the range, mean, median, mode, kurtosis, skewness, and standard deviation.

  • EC North test scores: 150, 122, 183, 197, 179, 165, 175, 162, 145, 128, 189, 172, 133, 190, 189, 125, 110, 170, 162, 152, 174, 190, 162, 147

  • EC Memorial test scores: 144, 190, 199, 140, 134, 176, 180, 190, 109, 135, 167, 118, 149, 190, 115, 194, 156, 122, 165, 172, 185, 149, 145, 194

  1. Create a histogram (or density plot) of both distributions and include them below (2 pts.).

  2. Eau Claire North (3.5 pts.)

    1. Mean:
    2. Median:
    3. Mode(s):
    4. Range:
    5. Standard deviation:
    6. Kurtosis:
    7. Skewness:

  3. Eau Claire Memorial (3.5 pts.)

    1. Mean:
    2. Median:
    3. Mode(s):
    4. Range:
    5. Standard deviation:
    6. Kurtosis:
    7. Skewness:

  4. Evaluate the public’s claim. Does it have any merit? Why or why not (2 pts.)?

Bonus (optional section)

  1. Create a density plot of both datasets on the same grid using ggplot2. Use colors other than the defaults, and make the densities slightly transparent (1 pts.).