## 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

- Center value within
- 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

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