Lesson 3: Measures of Center, Percentiles and Boxplots
August 27, 2024
Review:
 Attendance
 Visualizing the shape of the distribution
 Stemplots
 Histograms
 Against All Odds Video – Unit 3
 Demonstrate spreadsheet histogram construction
 Histogram ≠ Column Chart
 UN health and economy (Sheets)
 Cryptogram with frequency distribution – anyone solve?
Presentation:
 Measures of Center
 Mean
 Same as Average
 Sum of values divided by count, or ∑x/n
 n = total number of observations/measurements/values
 Example
 Median
 Center value within ordered sequence of values
 Same as 50th Percentile
 Position = 0.50*n
 n = total number of observations
 round to the nearest whole number
 alternative for small (n<30) data sets = (n+1)/2
 Example
 Video: Measures of Center
 Mean
 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 Female height data

 Boxplots
 Five number summary
 25th Percentile = Q1
 50th Percentile = Q2 = Median
 75th Percentile = Q3
 Minimum value
 Maximum value
 Range = Max – Min
 Interquartile Range (IQR) = Q3 – Q1
 Example with Male height data
 Video: Boxplots
Activity:
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 fivenumber 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 fivenumber summary.
d. Make a boxplot.
e. Compute the range and interquartile range (IQR).
These problem descriptions (#1 and #2) are from “Against All Odds”, modified slightly and copied here for convenience.
Problem 3.
Use the MPG data for top selling midsize cars in the US and European markets from Lesson 1.
a. Find the fivenumber summaries.
b. Produce 2 boxplots, one for each market, and put them both on the same chart to facilitate comparison.
Assignment:
 For class on Thu
 Use the UN health and economy data (filter to display North and South America only).
 Use Google Sheets (or Excel) to create a histogram for Life Expectancy, Infant Mortality and GDP Per Capita (3 separate histograms)
 Compute the 5number summary for Life Expectancy, Infant Mortality and GDP Per Capita (1 5number summary for each variable).
 Be prepared to share your histograms and 5number summaries.