math
AK47
Spring 2015, Math 130 Midterm Exam I N D E P E N D E N � S � U D � P R O J E C �
P ROBABILI�� & S �A�IS�ICS P ROJEC�
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.
�he 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.
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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
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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
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
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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).
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6: What is the probability of selecting a family grater that 507
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