Math 123
Fall 2017
Dr. Lily Yen
Assignment 3
Show all your work
Name:
Number:
Signature:
Score: /20
Problem 1: Below is a list of ages of 30 people in Kamloops who volunteered to help victims
of wild fire in BC this summer.
60, 69, 72, 62, 57, 66, 55, 69, 66, 72, 51,
74, 70, 58, 58, 53, 68, 53, 55, 53, 53, 59,
57, 51, 72, 65, 51, 60, 70 and 64.
a. Make a stem-and-leaf plot of the data.
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX4
XXXXXXXXXX
. Construct a relative frequency table using five classes.
Age Frequency Relative frequency
51– XXXXXXXXXX
56– XXXXXXXXXX
61– XXXXXXXXXX
66– XXXXXXXXXX
71– XXXXXXXXXX
Total 30
c. Draw a histogram from your relative frequency table. Clearly label the axes.
Age
R
el
at
iv
e
f
eq
u
en
cy
XXXXXXXXXX
0.1
0.2
0.3
Score: /6
Problem 2: In our class of 21, suppose 10 drive to Cap, 8 take public transit, and 3 walk.
Draw a pie chart for the above data. Include your steps for the calculation of each secto
angle in the pie.
Freq. Rel. freq. Angle
Drive XXXXXXXXXX
Transit XXXXXXXXXX
Walk XXXXXXXXXX
Total 21
Drive
Transit
Walk
Score: /3
Problem 3: Below is a list of 21 ages of the students from one of Lily’s classes.
20, 19, 22, 22, 27, 26, 25, 19, 26, 22, 21,
24, 20, 18, 18, 23, 18, 23, 45, 33 and 43.
Construct a box-and-whisker plot by computing the median, first and third quartiles com-
plete with the minimum and the maximum.
Min 18
1st Quartile 19.8
Median 22
3rd Quartile 26
Max 45
Mean 24.5
Mode 18, 22
XXXXXXXXXX
Score: /5
Problem 4: Using the same age data from the previous problem, compare its mode, mean,
and median.
Score: /2
Problem 5: The grade assignment on the curve is shown below where µ is the mean and s
is the sample standard deviation.
µ− 3
2
s µ− 1
2
s µ µ+ 1
2
s µ+ 3
2
s
F D C B A
XXXXXXXXXX98.4
Suppose the final marks in a class of ten students are 80, 76, 81, 94, 79, 60, 85, 100, 75 and
92. What grade does the person earning 79 get?
The mean is µ = 82.2 and the standard deviation is σ = 10.8. That leaves the ranges
indicated in the figure above. A 79 therefore earns a C.
Score: /4
Page 2 Math 123
Math 123
Fall 2017
Dr. Lily Yen
Assignment 3
Show all your work
Name:
Number:
Signature:
Score: /20
Problem 1: Below is a list of ages of 30 people in Kamloops who volunteered to help victims
of wild fire in BC this summer.
60, 69, 72, 62, 57, 66, 55, 69, 66, 72, 51,
74, 70, 58, 58, 53, 68, 53, 55, 53, 53, 59,
57, 51, 72, 65, 51, 60, 70 and 64.
a. Make a stem-and-leaf plot of the data.
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX4
XXXXXXXXXX
. Construct a relative frequency table using five classes.
Age Frequency Relative frequency
51– XXXXXXXXXX
56– XXXXXXXXXX
61– XXXXXXXXXX
66– XXXXXXXXXX
71– XXXXXXXXXX
Total 30
c. Draw a histogram from your relative frequency table. Clearly label the axes.
Age
R
el
at
iv
e
f
eq
u
en
cy
XXXXXXXXXX
0.1
0.2
0.3
Score: /6
Problem 2: In our class of 21, suppose 10 drive to Cap, 8 take public transit, and 3 walk.
Draw a pie chart for the above data. Include your steps for the calculation of each secto
angle in the pie.
Freq. Rel. freq. Angle
Drive XXXXXXXXXX
Transit XXXXXXXXXX
Walk XXXXXXXXXX
Total 21
Drive
Transit
Walk
Score: /3
Problem 3: Below is a list of 21 ages of the students from one of Lily’s classes.
20, 19, 22, 22, 27, 26, 25, 19, 26, 22, 21,
24, 20, 18, 18, 23, 18, 23, 45, 33 and 43.
Construct a box-and-whisker plot by computing the median, first and third quartiles com-
plete with the minimum and the maximum.
Min 18
1st Quartile 19.8
Median 22
3rd Quartile 26
Max 45
Mean 24.5
Mode 18, 22
XXXXXXXXXX
Score: /5
Problem 4: Using the same age data from the previous problem, compare its mode, mean,
and median.
Score: /2
Problem 5: The grade assignment on the curve is shown below where µ is the mean and s
is the sample standard deviation.
µ− 3
2
s µ− 1
2
s µ µ+ 1
2
s µ+ 3
2
s
F D C B A
XXXXXXXXXX98.4
Suppose the final marks in a class of ten students are 80, 76, 81, 94, 79, 60, 85, 100, 75 and
92. What grade does the person earning 79 get?
The mean is µ = 82.2 and the standard deviation is σ = 10.8. That leaves the ranges
indicated in the figure above. A 79 therefore earns a C.
Score: /4
Page 2 Math 123
chapter-statistics-qdxecysr.pdf
july19math123-0vge03ab.pdf
Example According to US government statistics, mononucleosis
(mono) is four times more common among college students than the rest
of the population. Blood tests for the disease are not 100% accurate.
Assume that Table 13.2 was obtained regarding students who came to
Capilano’s health centre complaining of tiredness, a sore throat, and
slight fever.
Has Mono No Mono Total
Positive test XXXXXXXXXX
Negative test XXXXXXXXXX
Total XXXXXXXXXX
Table 13.2: Test results for mononucleosis
Find the probability the student does not have mono, given that
the test is positive.
Practice exercises in Section 13.3: Every second odd from 1–59.
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Distinguish between disjoint (mutually exclusive) events and independent events.
Chapter 14: Descriptive Statistics
14.1 Organizing and Visualizing Data
Definition Statistics is the science of planning studies and experi-
ments, obtaining data, and then organizing, summarizing, presenting,
analyzing, interpreting, and drawing conclusions based on the data.
A common and important goal of is to learn about a
large group by examining data from of its members. For this
purpose, we need the following terms:
Terminology:
1. A population
2. A census
3. A sample
4. Data
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statistics
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a subset
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the entire collection of subjects under study
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is the study of entire population
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is a subset of the population, unbiasedly chosed
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a collection of information: there are two types, 1) qualitative, like hair colour, or ethnicity or make of ca
2) quantitative, numerical information
We learn to construct and interpret frequency tables of two types:
1. single value categories
2. grouped frequency tables
Definition A frequency distribution or frequency table shows
how a data set is partitioned among all of several categories (or classes)
y listing all of the categories along with the number of data values in
each of the categories.
Example Let us conduct a survey of the number of buses each student
needs to take to come to Capilano University in our class.
Now we organize it in a frequency table, i. e. for each category
(n buses), we count the number of students who take n buses fo
n = 0, 1, 2, 3, · · · . (See steps after example 2.)
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Example Let us survey our class for height in centimetres, then
organize our data according to the steps above. Let us first gather all
heights.
Below, we construct a table in five columns with the following
heading: height (cm), tally, frequency, (and relative frequency, and
cumulative frequency for later). Follow guidelines below for a frequency
table.
When you construct a frequency distribution to summarize a large
data set, the following steps can be helpful:
1. Determine the number of classes