MSM 709

Descriptive statistics and boxplots

Descriptive statistics: To find the mean, standard deviation and five-number summary of a data set, first enter the set into a list. Then, press STAT CALC and choose 1: 1-Var Stats The command is then pasted to the home screen. Input the list your data is in and press ENTER.

Boxplots

A boxplot (also called a box-and-whisker plot) is a visual representation of the five-number summary of a data set. The five-number summary consists of the maximum value, minimum value, median along with the first and third quartiles. The boxplot illustrates the spread of the different quarters of a data set. It is especially useful when comparing several data sets.

Problem: to create a boxplot first enter the data into a list.

1. Select STATPLOT. Turn the graph ON if you need to. Then choose boxplot (3^rd choice, which shows outliers, or 4^th choice, which does not.)

Press GRAPH. The window should be set from before. Press TRACE to indicate the values of the five-number summary.

Example: Height of buildings in Philadelphia and New York. (Resource: The World Almanac and Book of Facts, 2004)

The following is listing of the heights (in feet) of the 28 tallest buildings in Philadelphia.

490	491	739	412	492	945	572
548	435	435	492	400	700	400
375	405	848	390	482	475	572
490	364	375	792	500	384	450

For this data set, construct a histogram and boxplot, and describe the shape of the data set (symmetric, skewed left or right, bimodal, uniform?) Find the 1-Var Stats for this data set. Are there any outliers? Which gives a more accurate idea of the center of the data set in this case, the mean or the median?

Here is a set of the heights of the 28 tallest buildings in New York. Construct a boxplot and find the descriptive statistics, and compare to the Philadelphia data. Which city has the taller tall buildings? How did you decide?

700	705	707	716	724	725	730
739	741	743	745	750	750	752
778	792	808	809	813	814	850
856	861	915	927	952	1046	1250