Exam 1
Exam Page 1
Define each of the following:
a) Element.
An element is described as "the individual and unique entry in a data set about which data... [Show More] has
been collected, analyzed and presented in a same manner to differentiate" (Module 1).
b) Variable.
A variable is defined as a "particular measurable attribute that the researcher believes is needed
to describe the element in their study" (Module 1).
c) Data.
Data (or the plural of datumn) is defined as things (such as numerical information, people,
geographical areas,etc.) about which information can be collected and then analyzed.
Answer Key
Define each of the following:
a) Element.
a) The element of a data set is simply the individual and unique entry in a data set about which
data has been collected, analyzed and presented in the same manner.
b) Variable.
b) A variable is a particular, measurable attribute that the researcher believes is needed to
describe the element in their study.
c) Data.
c) Data are things about which information can be collected and analyzed.
Exam Page 2
Explain the difference between population and sample.
"The entire number of items in a large group" would be defined as the population. (Module 1)
The sample is then taken from the population by a researcher and is studied.The sample taken
from the population is, in fact, the subset of the population. You need the population to get the
sample and without the population, there can be no sample.
Instructor Comments
Very good definitions.
Answer Key
Explain the difference between population and sample.
Population is the entire number of items in a large group.
A sample is representative group from the population.
Exam Page 3
Look at the following data and see if you can identify any outliers:
65 71 55 69 3 77 67 70 246 61 277
3, 246, 277
Instructor Comments
Very good.
Answer Key
Look at the following data and see if you can identify any outliers:
65 71 55 69 3 77 67 70 246 61 277
The outliers are:
3 246 277
Exam Page 4
The following pie chart shows the percentages of total items sold in a month in a certain fast
food restaurant.
A total of 4900 fast food items were sold during the month.
How many were burgers?
How many were french fries?
4900(.32)=1568
32% or 1,568 burgers were sold during the month.
4900(.18)=882
18% or 882 french fries were sold during the month.
Instructor Comments
Very good.
Answer Key
The following pie chart shows the percentages of total items sold in a month in a certain fast
food restaurant.
A total of 4900 fast food items were sold during the month.
How many were burgers?
How many were french fries?
Burgers : 4900(.32) = 1568
French Fries : 4900(.18) = 882
Exam 2
Exam Page 1
During an hour at a fast food restaurant, the following types of sandwiches are ordered:
Turkey Hamburger Cheeseburger Fish Hamburger Turkey Fish
Chicken Fish Chicken Turkey Fish Hamburger Fish
Cheeseburger Fish Cheeseburger Hamburger Fish Fish
Cheeseburger Hamburger Fish Turkey Turkey Chicken Fish
Chicken Cheeseburger Fish Turkey Fish Fish Hamburger
Fish Fish Turkey Chicken Hamburger Fish Cheeseburger
Chicken Chicken Turkey Fish Chicken
Hamburger Chicken Fish Chicken
a) Make a frequency distribution for this data.
Types of Frequency
Sandwiches
Turkey 8
Chicken 10
Cheeseburger 6
Fish 18
Hamburger 8
Total 50
b) Make a relative frequency distribution for this data. Include relative percentages on this table.
Types of Frequency Relative Relative
Sandwiches Frequency Percentage
Turkey 8 (8/50)= .16 (.16)100= 16%
Chicken 10 (10/50)= .20 (.20)100= 20%
Cheeseburger 6 (6/50)= .12 (.12)100=
12%
Fish 18 (18/50)= .36 (.36)100= 36%
Hamburger 8 (8/50)= .16 (.16)100= 16%
Total 50 1 100%
Exam Page 2
Consider the following data:
422 389 414 401 466 421 399 387 450 407 392 410
440 417 490
Find the 20th percentile of this data.
387,389,392,399,401,407,410,414,417,421,422,440,450,466,490
i=(p n
= (20) *15= 3
100 ) 100
i=3
392 is the 20th percentile of this data.
Exam Page 3
Consider the following data:
{29, 20, 24, 18, 32, 21}
a) Find the sample mean of this data.
x* = ∑xi
n
x*=(29+20+24+18+32+21) =144=24
6 6
b) Find the range of this data.
{18,20,21,24,29,32}
Range is 14
(32-18)=14
c) Find the sample standard deviation of this data.
s
2=∑(xi -x)2 = (18-24)2
+ (20-24)2
+(21-24)2
+(24-24)2
+(29-24)2+
(32-24)2
= 36+16+9+0+25+64=
150=30
n-1 6-1 5 5
s=√s2
= √30 = 5.477
d) Find the coefficient of variation.
cov=standard deviation*100=5.477*100 =22.82
mean 24
Exam Page 4
Suppose that you have a set of data that has a mean of 65 and a standard deviation of 10.
a) Is the point 75 above, below, or the same as the mean. How many standard deviations is 75
from the mean.
x*65
z=x-u= 75-65=1
o 10
z=1
The point 75 is above the mean (because it is a positive number), meaning that the data point is
one standard deviation above the mean.
b) Is the point 85 above, below, or the same as the mean. How many standard deviations is 85
from the mean.
x*65
z=x-u= 85-65=2
o 10
z=2
The point 85 is above the mean (because it is a positive number), meaning that the data point is
two standard deviations above the mean.
c) Is the point 57.5 above, below, or the same as the mean. How many standard deviations is 57.5
from the mean.
x*65
z=x-u= 57.5-65=-0.75
o 10
z=-0.75
The point 57.5 is below the mean (because it is a negative number), meaning that the data point
is .75 standard deviations below the mean.
d) Is the point 107 above, below, or the same as the mean. How many standard deviations is 107
from the mean.
x*65
z=x-u= 107-65=4.2
o 10
z=4.2
The point 107 is above the mean (because it is a positive number), meaning that the data point is
4.2 standard deviations above the mean.
Exam Page 5
Consider the following set of data:
{22, 14, 35, 49, 8, 18, 30, 44}
a) Find the median.
{8,14,18,22,30,35,44,49}
Median=22+30=26
26
b) Find the mode of this set.
{8,14,18,22,30,35,44,49}
No mode (no number appears more than once).
Exam 3
Exam Page 1
Suppose A and B are two events with probabilities:
P(A)=.35,P(Bc
)=.45,P(A∩B)=.25.
Find the following:
a) P(A∪B).
P(AUB)=P(A)+P(B)-P(AnB)
P(Bc
)=> P(B)=1-P(Bc
)=1-.45=.55
P(AUB)=.35+.55-.25=0.6 [Show Less]
