Warm Up – Day 2 Stats Unit
3
1.
 3i 
2.
i 1
5
3.
5
 2i
2

4.
i 1
 (3i  1)
i 1
2

i 1
4
4
5.
 i
2

 (2i)
i 1
2

Central Tendency
Objective:
- Find the mean, median and mode of a set of data
- Draw a box and whisker plot to organize Real Life data
- Read and interpret a box and whisker plot of Real Life data.
Remember from last class…
Mean
Average
Middle number (or average of the 2 middle terms) in a set of data arranged least to
Median
greatest.
Mode
Most often repeated number in a set of data
Box and Whiskers Plot: A graphical representation of data based on quartiles and the
range of the data. A quartile is one of four equal parts of a group of data.
Median
Middle number (or average of the 2 middle terms) in a set of data arranged least to
greatest.
Quartile 1/4 of a set of data arranged least to greatest.
Min
Least number in a set of data arranged least to greatest.
Max
Greatest number in a set of data arranged least to greatest.
What would a box-and-whisker plot look like for the following data set?
{ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 }
Min:
_
Quartile 2 (Q1):
_
Median (Q2):
_
Quartile 3 (Q3):
_
Max:
_
Min:
Q1:
Median:
Q3:
Max:
Now do one on your own:
Using the data set { 11, 19, 5, 34, 9, 25, 28, 16, 17, 11, 12, 7 },
a) Arrange the data in increasing order:
b) Divide the numbers into 4 sets:
c) Calculate the 1st, 2nd, and 3rd Quartiles:
(FYI: 2nd quartile is the median. 1st & 3rd quartiles are the median of each half of the data.)
1st Quartile:
2nd Quartile:
3rd Quartile:
d) Draw a number line placing points at: Least number, 1st, 2nd, and 3rd Quartiles, and the
Greatest Number. What is the range of the data? _______
x
Now let’s learn how to use the calculator
to analyze and plot a data set!
Box-and-Whisker Plots on the TI-Nspire
Create a box and whisker plot to represent the following data set:
{85, 100, 97, 84, 73, 89, 73, 65, 50, 83, 79, 92, 78, 10}
There are two forms of box-and-whisker plots -- standard and modified.
The standard box-and whisker plot includes ALL data points, including what
are called outliers. Outliers are points that are far left or far right of the data set
and may detract from a representative picture of the data. Outliers are points
that are 1.5*IQR beyond the quartiles. (IQR stands for the Interquartile Range
which is Q3 – Q1.)
The modified box-and-whisker plot will not plot outliers as part of the boxand-whisker. The outliers are plotted as individual points beyond the whisker
in an attempt to give a more accurate picture of the dispersion of the data. The
modified style is the default on the TI-Nspire CX calculator.
Standard box plot.
Modified box plot.
These two plots represent
the same set of data.
1. Create new spreadsheet
Turn calculator on and press
following menu options:


or select the
1: New Document
4: Lists & Spreadsheets
This will create a new spreadsheet to hold our data and
highlight cell A1. The highlight means that the cell is
ready to receive a value.
2. Enter the data
Enter the first data point, then press
. The
calculator will automatically highlight the next cell
down in the column, A2. Continue entering data
points and pressing the enter key after each one until
the entire dataset has been entered.
3. Name the dataset
Now we need to name the data. Press ▲ until you
reach the top of the column, type "data", then press
enter.
4. Perform statistical analysis
Press
options:



and then select the following menu
4: Statistics
1: Stat Calculations
1: One-Variable Statistics
Press OK (center of touchpad) for both of the dialog
boxes that appear. By default, all the statistical analysis
information will be placed in columns B and C.
5. Locate the desired statistics
Find the following statistical information about this dataset (use the arrows keys on the touchpad to move
around the spreadsheet).
Mean (x̅): _________
Min (MinX): _________
First quartile (Q1X): _________
Median (MedianX): _________
Max (MaxX): _________
Third quartile (Q3X): _________
6. Create a Data & Statistics page
Press
and choose
.
At first, a generic statistics graph will appear. The
dataset points are randomly displayed because we have
not defined a variable to plot against. The value of
each point is shown next to it.
7. Set variable to plot against
Move the cursor to hover over the Click to add
variable at the bottom of the screen. Click on it.
Choose data from the choices.
The points will animate and rearrange themselves on a
Dot Plot according to the new variable we have chosen
to plot against.
8. Change Dot Plot to Box-and-Whisker Plot
Press


then select:
1: Plot Type
2: Box Plot
This is a modified box-and-whisker plot with the
outlier separated from the rest of the data display. The
default setting for box-and-whisker plots is to display
outliers, but we are not going to work with outliers. So
we must first change this plot property.
9. Change setting to not display outliers
Put cursor over white area of plot and press
. From the popup menu, select:

4: Extend Box Plot Whiskers
We now have a standard box-and-whisker plot!
10. Explore our Box-and-Whisker Plot!
As you move the cursor and hover over the box-andwhisker plot, from left to right you will see the values
for the minimum, first quartile, median, third quartile,
and the maximum.
11. Show points
Click on a box or whisker to display the points that
make up that portion of the plot.
12. Moving points
If you grab and move any of the data points, the graph
will change, the data information displayed for the
graph will change and the list in the Lists &
Spreadsheets will change.
Modified from original at mathbits.com ( http://mathbits.com/MathBits/TINSection/Statistics1/BoxWhisker.html )
Try these!
Draw a box and whisker plot of each data set and label the significant points.
Choose an appropriate scale as you record these on your notes!
1) The lengths of songs on a CD (in seconds)
{ 173, 206, 179, 257, 198, 251, 239, 246, 295, 181, 261 }
Min =
Q1 =
Q2 =
Q3 =
x
Max =
2) Hours worked per week:
{ 15, 15, 10, 12, 22, 10, 8, 14, 18, 22, 18, 15, 12, 11, 10 }
Min =
Q1 =
Q2 =
Q3 =
Max =
x
Stem-and-Leaf to Box-and-Whisker (SOL A9)
For the first time in history two African-Americans won best actor and actress at the Oscars on March 25,
2002. Denzel Washington was 47 years old when he won this Oscar and Halle Berry was 33 years old.
Below is a stem-and-leaf plot showing the ages of 72 recent Oscar-winners.
Activity 1
a. Find the 3 measures of central tendency for the ages of the 36 actresses. Round all measures to
the nearest tenth.
b. Now find the 3 measures of central tendency for the ages of the 36 actors. Round all measures to
the nearest tenth.
Activity 2
a. Use the measures of central tendency you just found to write a paragraph comparing the two sets
of data.
Activity 3
a. Construct a double box-and-whisker plot of the data for the ages of Oscar winning actors and
actresses in the box below.
Activity 4
a. Determine the typical age of an Oscar-winning actress. Now do the same for an Oscar-winning
actor. Use the box-and-whisker plot and the measures of central tendency to support your
generalization.
Box-and-Whisker Questions
1.
2.
3.
4.
5.
Central Tendency Homework
Identify the median of the data.
1. 10, 14, 11, 15, 17
2. 120, 110, 114, 128, 108, 106, 140
Identify the median, quartiles, and interquartile range of the data from the box-and-whisker
plot.
3.
4.
In Exercises 5–8, use the box-and-whisker plot.
5. About what percent of the data are greater than 26?
6. About what percent of the data are less than 21?
7. About what percent of the data are greater than 16?
8. Are there any outliers in the data? If so, explain how you know.
9.
10.
11.
12.