Mini Lesson 3 (Instruction)

Compare groups with box and whisker plots

Data Literacy Project

West Penobscot Bay Buoy

Background: There are 16 monitoring buoys in the Gulf of Maine.

The buoys automatically track conditions such as air temperature wave height wind speed & wind direction water temperature (at 1m, 2m, 20m, & 50m depths)

The data are sent in real-time via satellite so you can check the current conditions at any of the buoys via the Internet (http://www.neracoos.org/gomoos)

The buoys are sponsored by The National Oceanographic and Atmospheric Administration (NOAA) and the University of Maine, the Gulf of Maine Research Institute and other organizations.

The data can help answer questions like:

How do air and water temperatures compare at the West Penobscot Bay buoy?

Dot plot and box and whisker plot showing hourly air temperature measurements at the West Penobscot Bay buoy for one week during October, 2012. (24 hours X 7 days = 168 measurements!)

How variable was the air temperature during the week?

Anatomy of a box and whisker plot

MedianWhisker Whisker

Inter-quartile range (IQR)(“the box”)Axis title & units

Temperaturescale

Outliers

How variable was the air temperature during the week?

The MEDIAN is the exact middle of the data set. Half of the data points are above the median, and half are below.

How variable was the air temperature during the week?

The INTER-QUARTILE RANGE (IQR) is the length of the box. The middle 50% of the data points lie within the box. The length of the box shows how tightly the middle half of the data are clumped together.

25th

percentile 75th

percentile

50% of the temperatures were between 50° and 56°F

How variable was the air temperature during the week?

The RANGE is from one end of the whiskers to the other (including any outliers that may be present).

The outliers are in the bottom (or top) 5% of the data points. They are real events, so don’t throw them out!

5th percentile

The temperature ranged about 22°F

(between 38° and almost 60° F).

Box plots make it easy to compare two groups and decide if they are the same or different.

A box plot scale can be oriented either verticallyor horizontally.

How did air temperatures compare with water temperatures during the week?

The bottom graph shows the water temperatures at the same time the air temperatures were recorded at the buoy.

How did air temperatures compare with water temperatures during the week?

Air temps had a greater range (21°) than water temps did (3°).

The median water temp was warmer than median air temp.

The water temp box (the middle 50% of the

data or interquartile range) is shifted to the right of the air temp box and they don’t overlap very much.

The water temp box is much shorter than the air temp box is. That means the water temperatures did not vary from the median as much as the air temperatures did.

Claim: Water temperatures at the buoy during the week were mostly warmer and were much less variable than air temperatures were.

Practice: Ice-out dates

Question: How does the timing of ice-out on Moosehead Lake compare with the timing of ice out on Swan Lake?

Is the timing of ice-out the same or different at the two lakes?

Julia

n D

ay*

*Julian Day is the number of the day in the year, counting from January 1. Feb 1 = Julian Day 32

Background: The box plot shows the day of the year when the ice went out at each lake for the last hundred years or so.

How does the timing of ice-out on Moosehead Lake compare with the timing of ice out on Swan Lake?

• The lakes have similar ranges for ice-out dates, about 45 – 50 days, but the range for Moosehead is shifted above (later than) Swan L.

•The median ice out date at Moosehead is much later than the median date at Swan Lake. It is above the Swan Lake box.

•The inter-quartile ranges (boxes) have similar length, so the ice- out dates vary about the same at each lake…but…

•The inter-quartile ranges (boxes) don’t overlap at all. Most of Moosehead lake dates are later than Swan Lake dates.

Julia

n D

ay*

Are the lakes the same or different? They have similar variability, but the ice tends to go out later on Moosehead Lake.