6.SP

Warm UpUse the data below for Questions 1-4.14, 25, 37, 53, 26, 12, 70, 31

1. What is the mean?2. What is the median?3. What is the mode?4. What is the range?

Course 2

6.SP

The five number summary is another name for the visual representation of the box and whisker plot.

The five number summary consist of :◦ The median ( 2nd quartile)◦ The 1st quartile◦ The 3rd quartile◦ The maximum value in a data set◦ The minimum value in a data set

The table shows the stopping distances of different vehicles from 60 mi/h.

Course 2

Box-and-Whisker Plots

A 120

B 158

C 142

D 131

E 128

F 167

G 136

VehicleStopping Distance (ft)

To show the distribution of the data, you can use a box-and-whisker plot… see the next slide.

Course 2

Box-and-Whisker Plots

lower extreme, or minimum value

first quartile, the median of the lower half of the data set

110 120 130 140 150 160 170 180

second quartile, the median of the data set

third quartile, the median of the upper half of the data set

upper extreme, or maximum value

Step 1 - Find the median. Remember, the median is the middle value

in a data set.

18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

68 is the median of this data set.

Step 2 – Find the lower quartile. The lower quartile is the median of the data

set to the left of 68.

(18, 27, 34, 52, 54, 59, 61,) 68, 78, 82, 85, 87, 91, 93, 100

52 is the lower quartile

Step 3 – Find the upper quartile. The upper quartile is the median of the data

set to the right of 68.

18, 27, 34, 52, 54, 59, 61, 68, (78, 82, 85, 87, 91, 93, 100)

87 is the upper quartile

Step 4 – Find the maximum and minimum values in the set.

The maximum is the greatest value in the data set.

The minimum is the least value in the data set.18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93,

100

18 is the minimum and 100 is the maximum.

Step 5 – Find the inter-quartile range (IQR). The inter-quartile (IQR) range is the

difference between the upper and lower quartiles.◦ Upper Quartile = 87◦ Lower Quartile = 52◦ 87 – 52 = 35◦ 35 = IQR

Organize the 5 number summary◦ Median – 68◦ Lower Quartile – 52 ◦ Upper Quartile – 87 ◦ Max – 100 ◦ Min – 18

Notice, the Box includes the lower quartile, median, and upper quartile.

The Whiskers extend from the box to the max and min.

The data values found inside the box represent the middle half (50%) of the data.

The line segment inside the box represents the median

Use the following set of data to create the 5 number summary.

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

What is the median or 2nd quartile?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The median is 39

What is the lower or 1st quartile?

(3, 7, 11, 11, 15, 21, 23), 39, 41, 45, 50, 61, 87, 99, 220

The lower quartile is 11

What is the upper or 3rd quartile?

3, 7, 11, 11, 15, 21, 23, 39, (41, 45, 50, 61, 87, 99, 220)

The upper quartile is 61

What is the maximum?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The max is 220

What is the minimum?

3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

The min is 3

Take out your graph paper so we can practice graphing the data.

1.Draw a number line. Choose an appropriate interval and label your number line.

2.Graph each of the values in the 5 Number Summary onto your number line.

3.Draw a box around the upper and lower quartile and draw a vertical line through the median.

4.Extend whiskers to the extreme points.

Median - 39 Lower Quartile - 11 Upper Quartile - 61 Max - 220 Min - 3

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. The following slides show you how to interpret and describe your box plot.

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 graphQuartiles - 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.

Miles per Gallon of 4-cylinder Cars

20 24 28 32 36 40 44 Miles per gallon (mpg)

The Box and Whisker Plot clearly shows that there is a lot of different gas mileages on various 4-cylinder vehicles. 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. 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. The median cuts the data in half. The median is 32 mpg. Therefore half the cars in the study received 32 mpg.

On Your Own

Use the data for Questions 1-3.

24, 20, 18, 25, 22, 32, 30, 29, 35, 30, 28, 24, 38

1. What is the range?

2. What is the 3rd quartile?

3. Create a box-and-whisker plot for the data.

20

31

Course 2

Box-and-Whisker Plots

http://www.youtube.com/watch?v=CoVf1jLxgj4

Create a 5 Number Summary and Box Plot for the following quiz scores on our most recent quiz.

65, 72, 69, 87, 91, 74, 88, 99, 82, 65, 98, 100

1.