96 Math 116 – 02: Test #1 (Chapters 1 – 4)
Name:
Show work when possible to receive full credit for correct answers.
Give grammatically correct and clear explanations when asked to explain anything.
Each of #1 - #6 is worth 4 points.
1. School administrators collect data on students entering the university.
following variables are quantitative?
Which of the
(a) grade point average
(b) gender
(c) SAT score
(d) both (a) and (c)
(e) none of the above
2. The advantage of a stem-and-leaf display over a histogram is that a stem-and-leaf display
(a) satisfies the area principle.
(b) shows the shape of the distribution better than a histogram.
(c) can be used on categorical variables as well as quantitative variables
(d) preserves the individual data values.
(e) A stem-and-leaf display has no advantages over a histogram
3. Which is true of the data summarized in the histogram shown?
(a) The mean is less than the median.
(b) The data is skewed to the right.
(c) A boxplot for this data would have high outliers.
(d) The mean and standard deviation are good choices for center and spread.
(e) None of the statements above are true.
4. Which of the following data summaries are changed by adding 10 to each data value?
I. mean
II. median
III. range
IV. IQR
V. standard deviation
(a) I and V
(b) II and IV
(c) I and II
(d) III, IV, V
(e) all of them would change
5. The five number summary for a certain data set is as follows:
Min = 10, LQ = 15, MED = 16.5, UQ = 18, Max = 22
What can be said about this data set?
(a) there is at least one low outlier
(b) there is at least one high outlier
(c) there are no outliers
(d) there are both low and high outliers
(e) none of the above can be determined from the information given
6. We may choose to use a stem-and-leaf plot over a boxplot because a stem and leaf plot
I. reveals the shape of the distribution.
II. is better for large data sets.
III. displays the actual data.
(a) I only
(d) I and II
(b) II only
(e) I and III
(c) III only
(f) I, II, and III
(g) There is no advantage to a stem-and-leaf plot over a boxplot
7. The data below represents the sugar content (in grams) in one serving of 25 randomly
selected breakfast cereals. The stem is the 10’s digit.
0
0
1
1
2
2
3
3
1
5
0
5
1
6
0
6
1
1
8
2
1
8
3
2
8
2
8
3
9
3
4
4
0
(a) Complete the frequency table below.
Bin
Frequency
(12 points)
Relative
Frequency
0 to <4
4 to <8
8 to <12
12 to <16
16 to <20
20 to < 24
24 to <28
28 to <32
(b) Construct a histogram for this data using the same bins as is in (a).
(c) Find the mean and standard deviation for this data set.
(4 points)
(8 points)
(d) Give the five number summary of this data set.
(e) Construct a boxplot for this data set.
(5 points)
(8 points)
8. The boxplot below was constructed from the scores (out of 240 points) achieved by a random
sample of students in an AP Calculus class.
If we were to describe the center and spread of this data set, would it be better to do so with
mean and standard deviation or with median and IQR? Explain. (10 points)
9. The article “Motion Sickness in Public Road Transport: The Effect of Driver, Route, and
Vehicle” (Ergonomics [1991]: 1646 – 1664) reported that seat position within a bus may
have some effect on whether one experiences motion sick. The table below classifies each
person in a random sample of bus riders by the location of his/her seat and whether nausea
was experienced. (5 points each)
Nausea
No Nausea
Total
Front
58
870
928
Middle
166
1163
1329
Rear
193
806
999
Total
417
2839
3256
(a) What percent of the sample sat in the rear of the bus?
(b) What percent of the sample experienced nausea?
(c) Of those that did not experience nausea, what percent sat in the middle of the bus?
(d) Of those that sat in the middle of the bus, what percentage did not experience nausea?
(e) Of those that experienced nausea, what percentage did not sit in the rear?