Statistical Analysis
For Graphing Calculators

Send questions and comments concerning this lesson to author
Stephany Faulkner.

Grade Level:

Algebra 1 - TI-82/83 proficiency needed

Standards:

AI.8

Objective:

      To use data from the Chesapeake Bay; temperature, phosphate, nitrates, salinity, oxygen, and to analyze.

Procedure:

      Divide the class into groups no larger than 4. Students can enter their data into their calculators.
      We will be using Chesapeake Bay Temperature Data for 1986. All groups will start with the same data to make sure there is calculator understanding. Later each group can be given their own data.

Enter as follows:

Stat Edit

      Now several columns appear, labeled L1, L2 , L3, etc.. If there is any existing data, move the cursor so that it highlights L1 (or which ever column has data), press    clear, now move the cursor down to enter data. All existing data will be gone.

      The temperature for 1986, will now be entered into L1. After the 12 temperatures have been entered, one can look at the statistical analysis of the information.

Press:

Stat calc

      An entire new menu appears-- we are going to :

1-var stats

... but first, always check the set-up. This assures that the information being analyzed is done correctly.

Press       3 setup calc (appears on the screen)

xList - L1 must be highlighted (this is where we put our temperature)
freq - Do not Adjust

Press:

stat calc - 1-var statEnter

      A lot of new data has just appeared.

x -- mean value of x
mean is the average of adding all the numbers and dividing by the number of numbers

x -- Sigma
Sum of the x values - the calculator has taken all the x-values and added them together

x2 -- All the x's have been squared and then added together

Sx -- Sample standard deviation of x

x -- population Standard deviation of x

n -- Number of entries in your list (L1)

minX -- tells you the least value for x entered into L1

Q1-- 1st quartile ( we will see this again)

Med -- Median number -- this is different from mean as it is the number in the middle
An entirely different average from the mean (we will see this again)

Q3 -- 3rd quartile (we will see this again)

maxX -- highest number in our L1 list

      Now that we have analyzed our data, lets look at it graphically.

Press

window

      Since we are going to do a box and whisker plot, we are only interested in X on the window menu.

Xmin = 0 (slightly less than the lowest value of X in our L1 list)

Xmax = 30 (slightly higher than our highest value of X in our L1 list)

Xscl = your choice 1,2,3, etc.. It all depends on how you want your graph to look.

To graph

2nd Y=

Stat plot appears at the top of your screen

      Make sure all your plots are off before you turn any on. Press 4

Plots Off appears on screen with a flashing cursor.

Press enter

Done appears on the screen.

      This tells you all plots are off.

Press

Y= and ...
... clear any information that may be present here.

Press        2nd y=

Stat Plot (appears again)

#1 is highlighted (enter)

Plot 1 (appears on your screen)

cursor is flashing over ON
enter

Type:   3rd picture over needs to be highlighted.
enter

This is the box and whisker plot.

      When you pressed enter notice that several lines disappeared. This is because they are not needed in a box and whisker plot.

Xlist -- L1 must be highlighted as this is where we inputted our data.

Freq is defaulted at 1 - Do not change.

now Press

GRAPH

      A box and whisker plot now appears on your screen.

Press

TRACE

      You will notice that the cursor is flashing at the line in the middle of the graph. At the bottom left corner of the screen

med = with a number

      This is the median of the data. This is the same as the median we obtained with the 1-var statistics

Press   

>
   it will automatically take you to Q3 = a number. This is the same as in 1 - var statistics.

Press   

>
   one more time and it will take you MaxX. This is the maximum value for X in our L1 list.

<

      If you press    <    two times you will be back to the median.

Press   

<
   again , you will be at Q1 and one more time you will be at the minX. You will note these also match the 1-var statistics.

      You may graph up to three box and whisker plots at one time. By using your arrow keys you can move between them comparing values. If you plot two, remember that the first is in the middle and the second one is on the bottom. If you plot three, the first is on top, the second in the middle, and the third on the bottom. Be sure to adjust your window as necessary so that you will be able to view all three graphs.

      I have plotted three temperatures. Students can immediately note that the medians are different, but now 1987 and 1988 are very close. In 1986, the median temperature was much higher. You can have groups comparing temperature and oxygen.

      If you put Salinity into a list and create a Box and Whisker plot you will notice a dramatic change to the shape. It is much smaller. What does this mean anaylitically?

Extensions:

      There are five sets of data that follow this lab; 2 for temperature, one phosphate, one salinity, and one dissolved oxygen. Each comes with data for five years and the location in the bay where the data was obtained.

      In an Algebra One class, there are infinite possiblitilites with this data. One group could compare temperature at different parts of the bay and different years or another group could compare oxygen, phosphate and salinity in the same year looking at the size of the Box and Whisker plot.

      Be creative and resourceful, you have been given a lot of data. There's even more for you to use.