2 HOMEWORK ANSWERS
Important note about homework: Please be sure you submit your homework questions in order, and you make
it obvious which questions you are answering. In an effort to save paper, you do not need to submit the
questions; you only need to submit your answers. Please be clear and concise when preparing your homework
assignment.
Important note about late homework: Late homework is to be turned into Say Young Kim either in person,
during class, during his office hours, or by placing it in his mailbox. If you put your homework in Say Youngs
mailbox, send him an e-mail immediately afterwards to notify him of such and to document when you turned in
your homework. It is your responsibility to turn your homework in to Say Young. Thus, other TAs will not
relay your homework to him.
Important note about early homework: If you anticipate not being able to turn in your homework before
lecture on the day that it is due, you may turn your homework in early. As is the case with turning in late
homework, early homework is also to be turned into Say Young Kim following the same procedure as described
above for late homework.
When reading this homework answer key: The grading TAs have inserted comments in this key to help give
you a better understanding of common mistakes and errors. Please pay attention to these comments; they will
help you understand why an answer is considered incorrect.
1. Identify and justify what level of measurement is being used for each of the following::
a. Assessing if a person is either an introvert or an extravert
i. This is a nominal level of measurement as you are putting people into either the category
of introvert or extrovert and are not ordering people based on any personality
dimension.
b. Ranking job applicants for a potential job
i. This is ordinal level of measurement as you are rank ordering people by job potential.
c. Assessing confidence in a jurors verdict on a self-report measure from 0-100, assuming that the
difference between adjacent units throughout the scale is the same and that 0 means no
confidence
i. This is a ratio level of measurement as you are measuring confidence on a scale that has
equal units as a score of 0 that indicates no confidence (a true meaningful zero point).
d. Assessing if someone is mildly excited or ecstatically happy about stats.
i. This is a ordinal level of measurement as you ranking people in terms of how excited they
are about statistics with ecstatically happy indicating more happiness than mildly
excited
e. Depression using skin conductance measures that record the electrical resistance of skin,
assuming that the difference between adjacent units throughout the scale is the same.
i. You could make an argument here for either ratio or interval level of measurement so
either is accepted as long as you have a decent rationale.
f. Assessing confidence in a jurors verdict on a self-report measure from 0-100, assuming that the
difference between adjacent units throughout the scale is not the same.
i. This is a ordinal level of measurement as you are ordering people based on their stated
confidence with 100 being more confident than 90 but there are no equal intervals so it is
ordinal rather than interval.
g. Different types of coffee brought into stats class.
i. This is a nominal level of measurement as you are classifying the types of coffee that
people have, which does not allow for ranking of one type of coffee being greater than
another in terms of its coffeeness but instead just have categories of coffee.
h. Assessing speed of falling asleep.
i. This is a ratio level of measurement as time has equal intervals and a meaningful zero
point were a reaction time of 0 indicates no time.
Grading Note: Many students didnt justify their answers. Answering in context is desirable. Partial credit
was awarded if (1) your identification was one of the four options, even if you chose the wrong one; and (2)
your justification matched your identification if you chose the wrong one. Many students were confused on
parts (e) and (h).
2. For each of the following, indicate the real limits:
a. A heart rate of 130 (assume that the smallest unit of measurement is 10 pounds)
i. 125 - 135
b. A heart rate of 130 (assume that the smallest unit of measurement is 1 pound)
i. 129.5 130.5
c. A words with friends score of 99 (assume that the smallest unit of measurement is 1).
i. 98.5 99.5
d. A reaction time of 1.7 seconds (assume that the smallest unit of measurement is .1 seconds)
i. 1.65 - 1.75
e. A distance of 23.49 inches (assume that the smallest unit of measurement is .01 inches)
i. 23.485 - 23.495
Grading Note: Partial credit was awarded for being consistent in the amount added/subtracted to both upper
and lower limits. As a check, the distance between the true value and the upper limit should be the same as the
distance between the true value and the lower limit.
As you are enjoying a nice hot beverage indoors observing the snow finally falling this winter, you
notice that people appear to be helping one another in the snow. You decide to assess this and you assess
people on their community mindedness in the snow. Be sure to show all of your calculations. The
following data are the scores of the community sample on the community mindedness test:
91 51 94 74 67 91 73 63 75 84 89 76 66 94 84
3. You want to display your data in table format so you decide to do the following:
a. Create a grouped frequency distribution table from the raw data with 5 intervals. Make sure to
include real limits, midpoints, and all other information for a complete frequency distribution
table.
i. To create the grouped frequency table we must first determine the interval width: i =
range/number of intervals = (94 51)/5 =8.6, so we will round up to 9 as we want our
interval width to have the same lowest level of measurement as our data in this case
our lowest level of measurement is the ones place . Thus, our interval width is 9. Our
lowest observed score is 51 but 51 is not divisible by 9 so we go to the next lowest score
52, then 51, then 50, then 49, then 48, then 47, then 46, then 45 and we find that 45 is
divisible by 9 so we are going to make 49 our starting point: TABLE IS 12 POINTS
TOTAL
Apparent
Limits
45 - 53
54 - 62
63 - 71
72 - 80
81 - 89
90 - 98
Real
Limits
44.5 53.5 62.5 71.5 80.5 89.5 -
53.5
62.5
71.5
80.5
89.5
98.5
Midpoint
s
49
58
67
76
85
94
f
1
0
3
4
3
4
Rel f
0.07
0.00
0.20
0.27
0.20
0.27
Cum f
1
1
4
8
11
15
Cum Rel
f
0.07
0.07
0.27
0.53
0.73
1.00
Percenta
ge
7
7
27
53
73
100
*Note that we wanted to have 5 intervals but we ended up with 6 intervals. This occurred
primarily because we started at a different starting point than our lowest value: We started
at 49 instead of 51. In this case, however, even if we had stared at our lowest data point
and had no rounding we would still have ended up with 6 rather then 5 intervals! This
occurred because we used less a precise measure of range so our calculated range was
actually missing a score from our data. Instead of Maximum value Minimum value we
should do Maximum value Minimum value +1 to calculate range to encompass every
score. You were not expected to that for this and do not have to do this in the future, we are
merely explaining why this happened for your own education!
Grading Note: For full credit, you needed to show how you calculated the interval width (calculating 8.6 as
the width then rounding to 9); starting at 45 (a number divisible by 9) for the apparent limits, having consistent
interval widths in both the apparent and real limits; having correct values in each of the columns; and having
all of the columns present. Partial credit was awarded if you had the wrong values in a column but the column
as present.
b. What are the costs and benefits of grouped frequency distribution tables?
i. The benefit of the grouped frequency table is that it takes a bunch of numbers and
condenses them into a more meaningful and comprehensible display. The cost of the
grouped frequency table is that you lose information as you no longer see the raw data
but instead only know how many scores are in each group or interval.
Grading Note: Partial credit was awarded for attempting at least one cost and one benefit. You must have listed both a correct cost and a correct benefit for full credit.
4. Now you want to make your tables into graphs for ease of understanding, you decide to do the
following:
a. Using excel, make either a frequency bar graph or a frequency histogram of the data. Explain
why you chose to graph the data as you did, using issues discussed in class.
i. I would choose to make a histogram because my data are measured at the interval or
ratio level and histograms are more appropriate as they encompass the entire score
range.
Grading Note: For full credit, you must have picked a histogram, explained your choice, labeled x- and y-axes
appropriately (for instance, midpoints with context on the x-axis, frequency on the y-axis), used a meaningful title, used midpoints for x-axis values, and completed the graph completely in Excel.
b. Using excel, make a frequency polygon of the data.
FREQUENCY POLYGON IS 10 POINTS TOTAL
Grading Note: For full credit, you must have labeled axes in a similar manner to part (a), used an appropriate
title, closed the polygon by connecting the graph to the x-axis, found correct values for the high- and low-midpoint, and completed the graph using Excel.
c. Create a stem-and-leaf plot of your data in excel or by hand.
Stem
5
6
7
8
9
Leaf
1
367
3456
449
1144
Grading Note: For full credit, you must have labeled the columns as stem and leaf. You also must be sure
your leaves are in numerical order.
5. You are now interested in the central tendency of your data so you decide to do the following:
a. Calculate all three measures of central tendency.
i. Mean = (51+63+66+67+73+74+75+76+84+84+89+91+91+94+94)/15 = 78.13
ii. Median = 76
iii. Mode =84, 91, & 94
b. Discuss which measure you would report if you had to only report one measure.
i. In this instance I think the mean would be the best thing to report as it best
uses/represents all of the data and I dont think there are any extreme outliers in the
data.
Grading Note: You must be sure you report two digits after the decimal point. You must show all calculations
for full credit. It is important to note that the word average applies only to the mean. Be sure to be descriptive when talking about each measure of central tendency. Some students used vague descriptions or
definitions of each measure instead of providing an explanation. For the mode, all three values must be
present for full credit.
6. You are now interested in the interpretation of your data so you decide to do the following:
a. Looking at your tables, graphs, central tendency and variability, what can you say about the
data?
i. We can see that the scores have three modes and that most of the scores are in the 70s
or above. The average of the scores is 78.13 indicating that most of the data tend to
center in the upper 70s. However, we do not know if this indicates a high level of
community mindedness or not as we do not know the original scale. If the scale is 50
1,000 then this seems pretty low, but if the scale is 0 100 then this might be high. We
cant really interpret the data much without knowing the scale that it came from.
ii. As long as you talked about how the data are distributed and where they are located then
you should have gotten most, if not all points.
Grading Note: Many students missed the fact that the scale is not known fir this situation. For full credit, you
must mention the mean, median, and the mode and discuss the location of the data.
You are interested in the developing a new line of clothing for skydivers and want to know what age group
to focus your marketing towards for your new clothing line. You record the ages of people who come to a
nearby drop zone to skydive and you find the following:
18, 23, 24, 24, 23, 27, 29, 28, 24, 24, 21, 29, 30, 20, 27, 76
7. What one measure of central tendency would you report to your research team? Why? Calculate this
measure, report it and interpret it.
a. In this instance the median would be best to report because most score range between 18-30,
and then there is an extreme outlier of 76. If we calculate the mean, the measure of central tendency will be inflated and wont be as representative of the data.
b. The median is 24. There are 2 scores in the middle of the distribution because there is an even
number of participants. (24+24)/2 = 24
c. 24 represent the middle score of the distribution (i.e., the 50th percentile). For these data, the
median best represents the ages of people who skydive.
Grading Note: To earn full credit, you must have picked the median and provided an explanation in context.
You must have shown how to calculate whatever measure of central tendency you picked with a corresponding
explanation for partial credit.
You also recorded the style type of the people who came to the drop zone, and find the following:
Preppy, Grunge, Preppy, Preppy, Goth, Grunge, Preppy, Other, Goth, Preppy, Grunge, Preppy, Preppy, Preppy,
Goth, Goth
8. What one measure of central tendency would you report to your research team? Why? Calculate this
measure, report it and interpret it.
a. Here, you can only report the mode. Since your data are measured on the nominal scale, no other measure of central tendency would be available for your use.
b. The mode is Preppy with 8 counts of Preppy being the most frequently occurring style. This
means that of the people who came to the drop zone, the most frequent people who came to skydive had a preppy dress style.
Grading Note: For full credit, you must have picked the mode, stated the mode, and provided an explanation
in context. You must also interpret your score!