TASK #1Math II – Unit 4: Data Analysis and Probability

A math teacher must make a recommendation for a $2000 scholarship to a local chamber of commerce. The teacher has two students in mind Alan and Brianna. The teacher decides to let their grades be the determining factor.

Here are their test scores for the semester:

Alan: 90, 90, 80, 100, 99, 81, 98, 82Brianna: 90, 90, 91, 89, 91, 89, 90, 90

  1. Which student has the higher arithmetic mean, (average)?
  1. Which student has the higher median?
  1. What might be the problem of using these measures of central tendency?
  1. Consider using the measures of variability (or measures of spread) as a possible determining factor for the scholarship recipient.
  2. Find Mean Deviationb. Find Variance, .c. Find Standard Deviation.
Alan’s Data (Xi) / / / / Brianna’s Data (Xi) / / /
90 / 90
90 / 90
80 / 91
100 / 89
99 / 91
81 / 89
98 / 90
82 / 90
MEANS: / MEANS:
Should be Zero / Mean Deviation / Variation / Should be Zero / Mean Deviation / Variation
/ Standard Deviation / Standard Deviation

Calculator Task 1One Variable Statistics – Using Lists as a Mini-Spreadsheet

Calculating the Mean Deviation or Standard Deviation without the assistance of a spreadsheet can be tedious. The TI-83/84 calculator’s LISTS can be used to perform very similar tasks to those on a spreadsheet.

Let’s use the data from Brianna’s Grades above:

-First Reset the Stat Menu.

Press STAT, 5 , ENTER

-Go to the LIST Editor

Press STAT, 1

-Clear out any old data. Highlight the “L1” and press CLEAR, ENTER.

Press ▲ , CLEAR , ENTER. Clear out any old data in “L2” and “L3” also.

-Next, enter the data from CASE #2 in to “L1” as shown at the right.

-Move the cursor to the right ► and up ▲ until L2 is highlighted. Notice, the bottom of the calculator window should now show “L2=”. To create a new list

in L2 in which every data value of L1 is reduced by 50 simply press 2nd , 1 , – , 9 , 0 ,ENTER.

  • If the arithmetic mean wasn’t known at this time to be 90 we could have also used the calculator’s built in command to determine the arithmetic mean of L1. By instead pressing:

2nd , 1 , – , 2nd , STAT , ◄ , 3 , 2nd , 1 , ) , ENTER.

-Move the cursor to the right ► and up ▲ until L3 is highlighted. Notice, the bottom of the calculator window should now show “L3=”. To create a new list in which the absolute value is taken of each calculated difference in L2 press the

following : MATH , ► , 1 , 2nd , 2 , ) ,ENTER

-To calculate the mean deviation we only need to find the arithmetic mean of the data stored in L3. To do this press:

2nd , MODE, 2nd , STAT, ◄ , 3 , 2nd , 3 , ) ,ENTER

-Similarly we could calculate Population Standard Deviation, we could go back to the LIST menu by pressing STAT, 1 and high light L4. Then, to calculate the square of the difference simply pressing: 2nd, 2 , x2,ENTER (while L4 is highlighted)

Finally, we would need to calculate the square root of the arithmetic mean of the data in L4. To do this we must go back to the home screen again. Press the following.

2nd, MODE,2nd, x2 , 2nd , STAT, ◄ , 3 , 2nd, 4 , ) , ) ,ENTER

Fordata from Brianna’s Grades:

Mean Deviation = 0.5Pop. Standard Deviation (σx) ≈ 0.7071

  1. What does the difference in the measures of variability (spread) suggest?
  1. Using your measures, explain which student you think the teacher should choose and why.
  1. Matching:

Has a standard deviation of 0.A. 1, 7, 1, 7, 7,1

Has a standard deviation of 1.B. 1, 3, 1, 3, 1, 3

Has a standard deviation of 2.C. 4, –2, 8, 2, 4, 2

Has a standard deviation of 3.D. 1, 1, 1, 1, 1, 1

E. 5, 5, 5, 1, 1, 1

  1. Can you make a data set of 6 elements that has a standard deviation of 4?
  1. (BONUS) Can you make a data set of 6 elements that has a standard deviation of 4 but has more than just 2 unique elements?

If you were to take 10 coins and flip them and count the heads, how many coins would you expect to be heads up? Try a brief experiment. Flip 10 coins, count the number of heads that appear, write the number that appeared on a post it note. Finally, place the post notes on the board to create a frequency dot plot.

This is a great way to make a demonstration of an approximate normal distribution. However to create a large sample takes a long time.

Using Fathom a software program by Key Curriculum Press, you can simulate this event hundreds even thousands of time in a very short amount of time.