Spring 2015, Math 130 Midterm Exam

Spring 2015, Math 130 Midterm Exam

INDEPENDENT STUDY PROJECT

PROBABILITY & STATISTICS PROJECT

 

Directions.

 

In this project, you are going to graphically present and calculate statistics of a set of data that you gather. In addition, you will use the data to answer various probability/counting questions. The information below will instruct you on how to gather your data and what you will then do with the data.

 

The Data.

 

Collect the ages (in years) of all of your family members (parents, siblings) and extended family members (grandparents, aunts, uncles, cousins). Collect no more than 20 ages (in the case that you have a large family).

 

Graphically Presenting the Data.

You will present your data in several different ways. Use a separate sheet of paper for each.

 

1.Make a table that contains the name of the individual, their relation to you and their age.

 

2.Make a stem-and-leaf plot that displays all the ages in your set of data.

 

3.Make a stem-and-leaf plot that shows all the ages of males and females "back-to-back".

 

4.Make a histogram, that shows the number of individuals in the following age groups:

 

babies (0 - 1); children (2 - 12); teens (13 - 19); young adults (20 – 29); adults (30 - 69); seniors (70 +)

 

Statistics.

 

Calculate and show the following statistics for your data. Show all calculations in a neat and organized manner. Also, include labels for each calculation. Use a separate page for each item.

 

1.  a. Mean, median, mode, variance and standard deviation age for all data. b. Find quartiles and draw a box-and-whisker plot for all data.

 

2.  a. Mean, median, mode, variance and standard deviation age for all males. b. Find quartiles and draw a box-and-whisker plot for all males.

 

3.  a. Mean, median, mode, variance and standard deviation age for all females. b. Find quartiles and draw a box-and-whisker plot for all females.

 

Probability/Counting.

 

Using the date your collected, answer the questions that appear on the "Probability/Counting Questions" page. Show all work and answers in he space that is provided.

 

Project Materials/Assembly.

 

Other than the probability questions sheet, all work should be done on unlined or graph paper. Each page of the project should appear in the same order as mentioned in this document.


 

 

1


Include a title page for your project that includes your name. Staple the pages together in the upper left hand conner.

 

 

Grading.

 

Your grade will depend on your completeness, accuracy, neatness, organization, and presentation. This project will have the same weight of the midterm exam mentioned in the syllabus.

 

Due date: Monday _our project will be due: Monday, May 11th, 2015, at 1:00pm.

 

Examples

 

Example Table

 

Individual

Relationship to Me

Age

 

 

 

Jane Doe

Myself

18

 

 

 

Carol Doe

My Mom

42

 

 

 

Bob Doe

My Dad

45

 

 

 

Kate Doe

My Grandmother (Mom's side)

73

 

 

 

 

 

 

 

Example of Work & Work Labeling


 

Statistics of all males:

 

Mean:

1. Sum of ages

4 + 9 + 23 + 1 + 35 + 70 = 142

 

2.  Number of Males: 6

3.Mean age:

142/6 = 24

 

Median:

1. Ages in order:

1, 4, 9, 23, 35, 70

 

2.Middles two values: 9 & 23

3.Median:

(9+23)/2 = 16

 

4. Variance and standard deviation


 

 

Box and Whisker Plot for all females:

 

Median:

 

1. List all ages in order:

2, 5, 8, 19, 23, 39, 42, 69, 72

 

2. Median of all ages:

 

23 Lower Quartile:

 

1.  List all ages, lower than the median, in order: 2, 5, 8, 19

 

2.Median of lower ages:

(5 + 8)/2 = 6.5

 

Upper Quartile:

 

1.  List all ages, higher than the median, in order: 39, 42, 69, 72

 

2.Median of higher ages:

(42+69)/2 = 55.5


 

2


Example of a Poorly Drawn Box-and-Whisker Plot

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

P ROBABILITY /C OUNTING Q UESTIONS

 

Directions

 

Use the data that you have collected for your Probability & Statistics Project to answer the following questions. All work and answers should be done in the space provided.

 

Questions

 

Assume you put the names of each of your family members in a hat. The question below involves choosing a name or names from the hat:

 

1. What is the probability that you will select a person in the children or teen category7 Do the experiment! Repeat 10, 20, 50 times. What do your observe7 Compare your experimental results with your model (predictions).

 

 

 

2. What are the probability against you selecting a person from the children or teen group7

 


 

3. What is the probability of you choosing a person from the adult category, and then, without replacing the name, choosing someone from the children group7

 

 

 

4. What is the probability of you choosing a person from the young adults or adults group and then, after replacing the name, choosing someone from the children's group7

 

 

 

5. A driver picks up your family members at a family reunion. _he van holds 7 people, not including the driver. Assume the babies will not be riding in the van. How many different ways can 7 people be selected to ride in the van7 (hint: _he order is important).

 

 

 

6: What is the probability of selecting a family grater that 507

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