Box and Whisker Plots

SWBAT create, read, and identify the values of a box and whisker plot.

Warm Up

1. In Ms. Mayer’s language arts class, a group of students got the following scores on their MAP test: 208, 214, 220, 222, 225, 225, and 232. 1. Find the mean of the data2. Find the median of the data3. Find the mode of the data4. Find the range of the data5. Create a dot plot to display the data

Go over Dot Plots and Histograms

A box plot summarizes data using the median, upper and lower quartiles, and the extreme (least and greatest) values. It allows you to see important characteristics of the data at a glance.

Example Problem: The gas mileages in miles per gallon (mpg) of 4-cylinder manual transmission cars are in a table on the next slide

MPG of 4-cylinder cars28 32 42 37

30 25 44 38

24 32 33 44

38 34 30 44

31 28 31 29

39 29 32 29

24 25 28 28 29 29 29 30 30 31 31 32 32 32 33 34 37 38 38 39 42 44 44 44

Arrange the data in order from least to greatest.

24 25 28 28 29 29 29 30 30 31 31 32 32 32 33 34 37 38 38 39 42 44 44 44

Find the median of the data. It is 32This divides the data in half. The lower half : 24 25 28 28 29 29 29 30 30 31 31 32 and the upper half: 32 32 33 34 37 38 38 39 42 44 44 44

Find the median of the top half of the data.

32 32 33 34 37 38 38 39 42 44 44 44This is called the upper quartile or quartile 3. It is 38.

Take the lower half of the data and find the median of it.

24 25 28 28 29 29 29 30 30 31 31 32

This data, 29, is called the lower quartile or quartile 1.

Next, find the lower and upper extremes. (the lowest data, 24, and the highest data, 44).

Lower extreme = 24Lower quartile(Q1) =29Median (Q2) = 32Upper quartile(Q3) =38Upper extreme(Q4)=44

The data is now divided into quartiles(4ths) so each quartile represents one-fourth of the data.

Next, make a number line that will best display the 5 pieces of data (24 29 32 38 44)

20 24 28 32 36 40 44

Place a dot above the number line to show the lower extreme and for the upper extreme.

20 24 28 32 36 40 44

Put a vertical line above the number line for the median and one for the lower and upper quartiles.

20 24 28 32 36 40 44

Make a box out of the vertical lines and then from the box, draw a line to each dot.

20 24 28 32 36 40 44

You must label the number line to tell what the data represents.

Miles per gallon (mpg)

20 24 28 32 36 40 44

All graphs must have a title that clearly represents what your graph is showing.

Miles per Gallon of 4-cylinder Cars

20 24 28 32 36 40 44

Miles per gallon (mpg)

Interpreting the Box Plot:

Study your Box and Whisker Plot to determine what it is telling you. Make a statement about what it is saying, then support the statement with facts from your graph.

You should include the following in your interpretation:• Range or spread of the data and what it

means on your graph• Quartiles—compare them. What are

they telling you about the data?• Median- this is an important part of the

graph, and should be an important part of the interpretation.

• Percentages should be used to interpret the data, where relevant.

We will now interpret the data we have on mpg of 4-cylinder cars. We will do this step-by-step, then put all the interpretation together as our final summary.

Miles per Gallon of 4-cylinder Cars

20 24 28 32 36 40 44

Miles per gallon (mpg)

Make a statement about what it is saying, then support the statement with facts from your graph:

The Box and Whisker Plot clearly shows that are a lot of different gas mileages on various 4-cylinder vehicles

Miles per Gallon of 4-cylinder Cars

20 24 28 32 36 40 44

Miles per gallon (mpg)

Range or spread of the data and what it means to your graph

The mileage ranged from 24 miles per gallon(mpg) to a high of 44 mpg. This is a 20 miles per gallon spread, which in car mileage is quite a bit of difference.

Quartiles—compare them. What are they telling you about the data?

The first quartile reads as 32 mpg which means that 75% of the vehicles in this study got 32 mpg or more.

The 3rd quartile tells us that 25% of these cars got 38 mpg or higher which is really good mileage.

Median- this is an important part of the graph, and should be an important part of the interpretation.

The median cuts the data in half. The median is 32 mpg. Therefore half the cars in the study received 32 mpg or higher.