Math 112
Exam 1 Summer 2007
Full Name ______KEY____________
Show work for full credit!
ID# ___________
100points total
Good Luck!
I. (3pts) Define and give an example: (Please write neatly and concise.)
a) Parameter:
See book definition and example.
b) Sample: See book definition and example.
c) Population: See book definition and example.
d) Statistic (Note, this is not statistics): See book definition and example.
e) Standard Deviation: See book definition and example.
f) Random Sample: See book definition and example.
II. What is the difference between qualitative data and quantitative data? Be specific, give an
example of each. (7 points)
Qualitative data can be separated into categories that are distinguished by nonnumeric characteristics.
(Answers will vary) Example: Yes/No; Alive/Dead; Social Security Numbers; Colors of the rainbow.
Quantitative data consists of numbers representing counts or measurements. It breaks down into
Continuous and discrete data. (Answers will vary)Example: Weight of a person (continuous);
Number of students in school (discrete); Height of students (continuous); Number items in a shopping
cart( discrete).
Is the weight or height of your M112 professor a qualitative data?
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NO
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III. Provide the appropriate name for the following symbols: (2 points each)
a) Symbol _  :_Population mean
b) Symbol _
x
:__Sample mean_
c) Symbol _  _:__Population variance_
2
2
d) Symbol _ s _: __Sample variance_
e) Symbol __
 _:__Population SD_
f) Symbol _S_:__Sample SD__
IV. True or False (1 points each)
__T__Random Sample is a sample selected in such a way that allows every member of the population
to have the same chance of being chosen.
__F__If a sample has a standard deviation of 2.324, its variance is 1.524.
__T__Eye color would be an example of qualitative data.
___F__For every set of data, the value of the median will always be one of the original items of data.
__F_The sum of the squares of the deviations from the mean,
(x  x )
2
, will sometimes be negative.
__F__The standard deviation for the set of values 5, 5, 5, 5 and 5 is 5.
_F_The SD is 2.25, using the range rule of thumb for the set of values 1, 2, 3, 4, 5, 6, 7, 8.
V. Multiple Choices, circle correct answer. (2 point each)
1) The following set of data represents letter grades on a test in a Statistics class:
A,A,A,B,B,B,B,B,C,C,C,C,C,C,C,C,C,CC,D,D,D,D,F.
Select the most appropriate measure of central tendency for the data described.
a) Mean
b) Median
(c) Mode
d) Midrange
2) The measure most affected by extreme values is:
(a) Mean
Professor Seres
b) Median
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c) Mode
d) Midquartile
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VI. The sample data below is centimeters of rain per year in a South American country.
Box your answers! (14 points total)
21
19.5
19.75
29.5
23.5
13.5
Do the following:
a) Find the mean.
21.125
b) Find the mode:
no mode
c) Find the median: 20.375
d) Find the range:
16
e) Find the variance, show all work here:
s 
2
n(  x 2 )  (  x ) 2
n(n  1)

6(2816.0625)  (126.75) 2
 27.6938
6(5)
f) Find the standard deviation of the Quiz data set.
s= 27.6938  5.26
VII.
(2points each, 10 total)
Pulse Rate for M112 Students, Class # 20721
100
100
5
Pulse Rate( Bpm)
95
95
90
90
85
85
4
80
75
3
70
80
75
70
2
65
60
65
60
55
1
55
Identify the 5-number summary (approximate Pulse Rate is fine) from the Box Plot above and
interpret!
1. The lowest pulse rate among students of M112 class is 53 bpm .
2. The first quartile is 67 bpm. This means that 25 % of student have a pulse rate less then or equal to
67 bmp or 75 % of students have a pulse rate greater then or equal to 67 bpm.
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3._The second quartile is 75bpm. This means that 50% of students pulse rate is less then or equal to
75 bpm or 50% of students pulse rate is greater than or equal to 75 bpm.
4._The third quartile is 80bpm. This means that 75% of students pulse rate is less then or equal to
80bmp or 25% of students pulse rate is greater than or equal to 80bpm.
5.__The highest pulse rate among M112 students is 96 bpm. Note, there is an outlier of about 100bpm.
VIII. Use the given data to construct: a) frequency distribution, b) relative (%) frequency
distribution, c) cumulative frequency distribution, and a d) frequency histogram (label each
axis)
On a math test, the scores of 24 students were. (18 points total)
98
72
71
64
71
71
98
84
71
68
81
72
72
81
71
72
81
71
72
84
72
81
84
64
Use 4 classes beginning with a lower class limit of 60.
a) Math Test
Frequency
b) Math Test
Frequency (%)
c) Math Test
Cumulative Frequency
60-69
3
60-69
0.1250 =12.5%
60-69
3
70-79
12
70-79
0.5000= 50%
70-79
15
80-89
7
80-89
0.2917=29.17%
80-89
22
90-99
2
90-99
0.0833=8.33%
90-99
24
Sum
24/24
Sum
24
Sum
1
c) Interpret a section of the relative (%) frequency distribution from part (b) above: Answers may
vary. One answer could be: 50% of the student’s math scores fall between 70-79.
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F
r
e
q
u
12
E
n
c 7
y
S
c
o
r
e
s
3
2
59.5
69.5
79.5
89.5
99.5
Math scores
d) From the histogram above, identify the class with the tallest bar graph and interpret:
There are 12 students who received scores between 70-79 on the math test. The frequency of the tallest
graph is 12 the class is 70-79.
IX. Short answers. (2 points each)
1. What is our Elementary Statistics book author’s name: _Mario Triola_
2. Name another name for Mean: __Average____
3. Name another name for the Median: __Fiftieth percentile
4. What is considered an unusual value for z-scores:_
A z-score that is greater then 2 or a z-score that is less then -2.
5. What is considered a usual value for not z-scores?
It is any value that falls within x  2s
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