## Lesson 2: Measures of Center, Percentiles and Boxplots

August 27, 2018

Review:

- Math Assessment Results
- mean = 7.8
- median = 8
- mode = 8
- standard deviation = 2.2

- Stemplots (JH: put height data on whiteboard)
- Histograms
- Attendance

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

- Center value within
- Video: Measures of Center (4:40-7:55)

- 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
- 152, 157, 160, 165(2), 168, 170(3), 173(2), 180

**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
- 160, 168, 170(2), 173(3), 175(3), 177, 178(15), 180(4), 183(5), 185(4), 188(5), 191(4), 193, 196(2), 203

- Video: Boxplots (3:45-8:15)
- Examples

- Google Sheets
- Install Statistics “Add-On”
- Demonstrate Boxplots and Percentile calculations
- Use Student Height Data

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 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 (#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. Make a back-to-back stemplot.

b. Find the five-number summaries.

c. Produce 2 boxplots, one for each market, and * put them both on the same axes* to facilitate comparison.

Assignment:

- Boxplots in Google Sheets
- Use the data from Problems 1-3 (above) to make corresponding boxplots
- You will need to install the “Statistics” Add-On

- Text: Ch. 1 p. 30-38