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·        Names: Tania Stoker , Joseph  Omogrosso , William Kinch,  Becky Groce

 

 

Grade Level:  9—12                                Content Area :  Statistics / Data Analysis

 

 

PA standard(s) addressed :                        NCTM standards addressed :

2.6.A                                                  Data analysis and Probability

2.6.B

2.6.C

2.6.D

 

Problem Name : Leaping Lizards

 

 

Problem:

 

The following data was taken from Mr. Norman’s track team in which there are 10 students.

X= the height of the student and Y=is the distance of his/her jump.

The distance of the jumps has a mean of 56.7.

(72,57) , ( 69, 46) , ( 70,49) , (75,65) , ( 74,65) , (70,55) , (72,62) , ( 68,50) , (74,60) , ( 73,58)

 

 

 

Directions:      For full credit, you must do the following:

 

1.      Graph the data using a scatter plot and label the axes.

2.      Find the line of regression rounded to the nearest tenth.

3.      Find the standard deviation for the distance of the jumps.

4.      Find the upper and lower quartile for the distance of the jumps.

5.      Write an explanation stating the mathematical reasons why you chose each of your steps.

 

 

Problem Name:          Leaping Lizards

 

Grade Level:     9-12                                                                Content Area:    Statistics / Data Analysis

 

Problem Solution:

 

1.)                    SCATTER PLOT FOR DATA

 

 

 

   2.)          DETERMINE THE BEST-FIT LINE FOR THE DATA

 

 

Solution:          Y = 2.5X – 125.2

 

 

Calculator:               LinReg(ax + b), L1, L2          

(where L1 is the data for height and L2 is the data for distance of the jump)

 

 

By Hand:       Estimate the position of the regression line by eye or use the concept of median-median lines as a boundary.  Determine the equation for the line by finding the slope and y-intercept of the best-fit line.

 

 

 

3.)                    DETERMINE THE STANDARD DEVIATION FOR THE DISTANCE OF THE JUMPS

 

 

Solution:               Standard Deviation = 6.3

 

 

Calculator:             1-Var Stats L2 and look for Sx

 

 

By Hand:         Use the mean (X) which was given as 56.7 and the formula for standard deviation which is SQRT(S (Xi - X)2  / N) from i = 1 to N

 

=    SQRT {[(57-56.7)2 + (46-56.7)2 + (49-56.7)2 + (65-56.7)2 + (65-56.7)2 +

(55-56.7)2 + (62- 56.7)2 + (50-56.7)2 + (60–56.7)2 + (58 – 56.7)2] / 10}

=    SQRT (400.1 / 10)

=    6.3

 

 

 

 

4.)                    DETERMINE THE VALUES FOR THE UPPER AND LOWER QUARTILES

 

 

Solution:              Q1 = 50 and Q3 = 62

 

 

Calculator:             1-Var Stats L2  and look for Q1 and Q3

 

 

By Hand:               Arrange the values from least to greatest.  Since there are 10 values, Q1 is the 3rd value (50) and Q3 is the 7th value (62)

 

46        49        50        55        57        58        60        62        65        65

 

 

 

                        Q1                                                                           Q3

 

                 

           

Problem name: Leaping Lizards

 

Grade Level: 9—12                                        Content Area: Statistics/ Data Analysis

 

 

Specific Rubric:

 

5:         Have graph labeled properly and points in correct places

Correct answer of standard deviation rounded to the nearest tenth

Correct upper and lower quartile

Correct equation for line of regression  ( ± 0.5 for slope ,  ± 25 for y-intercept)

            All work shown and fully explained.

            Explanation includes why steps were performed .

            Nothing incorrect is shown.

 

4:         Have graph labeled properly and points in correct places

            Correct answer of standard deviation rounded to the nearest tenth

            Correct upper and lower quartile

Correct equation for line of regression  ( ± 0.5 for slope ,  ± 25 for y-intercept)

All work shown but minor omission in explanation or label.

 

 

3:         Have graph labeled properly and points in correct places

Correct answer of standard deviation rounded to the nearest tenth

Correct upper and lower quartile

Correct equation for line of regression  ( ± 0.5 for slope ,  ± 25 for y-intercept)

Most or all calculations shown but NO explanation.

 

                                                OR

 

Have graph labeled properly and points in correct places

Correct answer of standard deviation rounded to the nearest tenth

Correct upper and lower quartile

Correct equation for line of regression  ( ± 0.5 for slope, ±25 for y-intercept)

Some work and some explanation but it can be followed.

                                   

                                   OR

Incorrect answer with correct procedures shown or described and some explanation but one calculation error.

 

2:         Have graph labeled properly and points in correct places

            Correct answer of standard deviation rounded to nearest tenth

            Correct upper and lower quartile

            Correct equation for line of regression (± 0.5 for slope, ±25 for y-intercept)

            Some work or calculations shown

            4 – 5 correct with no work and no explanation.

 

                                               OR

 

           3 correct with some work, no explanation.

 

                                               OR

 

           2 correct with work and explanation.

 

                                              OR

 

Incorrect answer

Most work shown but 2 or 3 calculation errors

Some explanation.

 

                                             OR

 

Incorrect answer

2 errors in computation

No explanation.

 

1:         Have graph labeled properly and points in correct places

Correct answer of standard deviation rounded to the nearest tenth

Correct upper and lower quartile

Correct equation for line of regression   ( ± 0.5 for slope ,  ± 25 for y-intercept)

Work is missing completely, not readable or no work.

 

                                                OR

 

            1 – 3 correct answers, no work, and no explanation

 

                                               OR

 

           Some work or explanation that shows some understanding of the problem.

 
OR

 

Have one of the five parts correctly done with some explanation of why.

 

                              OR

 

Have two correct answers with some explanation.

 

                              OR

 

Have three correct answers with little or explanation.

 

                              OR

 

Have four or five correct answers with no explanation.

 

 

 

0:        Incorrect answers with nothing related to the problem.

 

                             OR

 

Nothing that indicates understanding of the problem

 

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