Lesson 2: Measures of Center and Boxplots

August 28, 2017

Review:

• Stemplots
• Histograms
• Assignment for Lesson 1
• Slack
  • student name with Slack username
• Attendance
• Tutoring Available
  • David Mould: [email protected]
  • Fridays 9-11 am in HSB 108 or by appointment

Presentation:

• Measures of Center
  • Mean
    • Same as Average
    • Sum of values divided by count, or ∑x/n
    • Example with height data
  • Median
    • Center value within ordered sequence of values
    • Same as 50th Percentile
    • Position = (n + 1)/2
      • n = total number of observations
      • Another approach with larger data sets, position = 0.50*n
      • If the position is between two numbers then take the average of those two values.
    • Example with height data
  • Video: Measures of Center

• Percentiles and Boxplots
  • Percentiles
  • To find the xth percentile
    • calculate x/100 * n (rounded to the nearest integer or take average of two values on either side)
    • result is the position of the value in an ordered (smallest to largest) data set
    • 25th percentile = 25/100 * n
    • 50th percentile = 50/100 * n = Median
    • 75th percentile = 75/100 * n
    • Example with height data
  • Boxplots
  • Five number graphic summary
    • 25th Percentile
    • 50th Percentile = Median
    • 75th Percentile
    • Minimum value
    • Maximum value
    • Example with height data
  • Video: Boxplots
  • Examples
    • Stacking Bar Charts, Histograms and Boxplots
    • Boxplot paired with Histogram

Assignment:

Problem 1.

Here are the starting salaries, in thousands of dollars, offered to 20 students who earned bachelor’s degrees in computer science in 2011.
63 56 66 77 50 53 78 55 90 65 64 69 59 76 48 54 49 68 51 50
a. Make a stemplot.
b. Find the median, mean and mode.
c. Find the five-number summary.
d. Make a boxplot.
e. Compute the range and interquartile range (IQR).

Problem 2.

A consumer testing lab measured calories per hot dog in 20 brands of beef hot dogs. Here are the results:
186 181 176 149 184 190 158 139 175 148 152 111 141 153 190 157 131 149 135 132
a. Make a stemplot.
b. Find the median, mean and mode.
c. Find the five-number summary.
d. Make a boxplot.
e. Compute the range and interquartile range (IQR).

These problem descriptions are from “Against All Odds”, modified slightly and copied here for convenience.

Please upload to Slack channel #lesson02

Study:

• Textbook Read Ch. 1 p. 30-38
• Preview:
  • Standard Deviation: AgainstAllOdds_StudentGuide_Unit06
  • Normal Curves: AgainstAllOdds_StudentGuide_Unit07