McGraw Hill Glencoe Algebra 1, 2012
MH
McGraw Hill Glencoe Algebra 1, 2012 View details
13. Representing Data
Continue to next subchapter

Exercise 4 Page p45

The following set of data is given.
We will make a stem-and-leaf plot and a box-and-whisker plot. To do that it will help to order the data values from least to greatest.
Now, we can start with stem-and-leaf plot.

Stem-and-Leaf Plot

In a stem-and-leaf plot, the digits of the least place value usually form the leaves, and the rest of the digits form the stems. Thus, we can make the stem-and-leaf plot as shown below.

Stem Leaf

Next we will make a box-and-whisker plot.

Box-and-Whisker Plot

To create a box-and-whisker plot, we need to identify five things.

  1. Minimum value
  2. Lower quartile
  3. Median value
  4. Upper quartile
  5. Maximum value
To find these values we need to have the data arranged from least to greatest.
Now we can immediately identify the and value.
The median is the value that is in the middle of the data set. Since the number of data values is an even number, there is no unique median. Instead, the median will be average of the data values that are closest to the middle
The median is the mean of the and value.
The lower and upper quartile is the value that is in the middle of the lower and upper half of the data set. Again we have to use the values that are closest to the middle. Let's mark these for the and quartile.
Now we can calculate the lower and upper quartile for the data set.
Let's summarize the information in a table.
Minimum value
Lower quartile
Median
Upper quartile
Maximum value

Now we can make our box-and-whisker plot.

Box-and-whisker plot of the data set

Outliers

In order to identify any outliers we will first need to find the interquartile range. The interquartile range is the range between the lower quartile and the upper quartile
Let's find the
Thus, the interquartile range is Now we will write two inequalities that determine the outliers,
Numbers less than and greater than are outliers. Since there are no outliers in the set of data, they do not affect the quartiles.