These are bunch of statistics questions anyone can practice to test their capability
in handling statistical data.Anyone can submit their answers using the comment box
to any of the questions and l’ll reply if its right or wrong. If you are have
problem solving any of the questions, please submit a request for the solution
using the comment box and l’ll reply with the solution.
1.A random sample of 98 high school students had their blood drawn. Their
blood types would be an example of what level of data? Circle the correct answer!
a.Ordinal b.Interval c.Nominal d.Ratio
2.A quantity computed from the values in a sample is called a : : :
Circle the correct answer!
a.Statistic b.Parameter c.Variable d.Sample e.Characteristic
3.For data that is nominal-level data, which of the following would be the ap-
propriate tool for representing the data graphically? Circle the correct answer!
a.Stem-and-Leaf Display b.Frequency Distribution c.Histogram d.Pie Chart
4.A garbage carrier would like to start charging by the weight of a cus-
tomer’s garbage rather than the number of cans. The weights (in pounds) of 90
randomly selected cans of garbage are summarized in the chart below.
Class Interval Frequency
1 [4:9; 8:9) 4
2 [8:9; 12:9) 11
3 [12:9; 16:9) 16
4 [16:9; 20:9) 27
5 [20:9; 24:9) 19
6 [24:9; 28:9) 10
7 [28:9; 32:9] 3
(a)Construct the frequency histogram. What is the shape of the histogram?
(b)What percentage of the cans weigh less than 20.9 pounds?
5.If a histogram is constructed for the following frequency distribution, what
shape would it have?
Interval Frequency
20 < x < 30 5
30 < x < 40 15
40 < x < 50 20
50 < x < 60 18
60 < x < 70 13
70 < x < 80 10
80 < x < 90 5
90 < x < 100 1
6.The following stem-and-leaf display shows the number of hours worked per
week by a sample of 25 students. What is the shape of this distribution?
Stem Leaf
0 0 0 0 0 1 2
1 0 2 2 4 5 7 7 8
2 1 1 6 7
3 0 2 5 leaf unit = 1 hour (ones)
4 0 0 2 stem unit = 10 hours (tens)
5 1
7.People with diabetes must monitor and control their blood glucose level. The
goal is to maintain “fasting plasma glucose” between about 90 and 130 milligrams
per deciliter. Here are the fasting glucose levels for 16 diabetics given individual
instruction on diabetes control:
128 195 188 158 227 198 163 164
159 128 283 226 223 221 220 160
Construct an appropriate stem-and-leaf display for this data and determine the shape
of the distribution.
8.A sample of eight doctors was asked how many flu shots they had given to patients
last fall. The numbers of flu shots were 6, 3, 5, 14, 2, 3, 0, and 8.
(a)Which measure of center would be more appropriate for this data set, the
sample mean or the sample median? Give an explanation of your choice!
(b)Compute the value of the measure of your choice
9.Another measure of center is the midquartile which is de
fined as the mean of the
first and the third quartile. What can we say about the position of the midquartile?
Circle the correct answer!
a.It is the median.
b.It is always below the mean.
c.It is always above the median.
d.It is always between the
rst and the third quartile.
f.It is always within one standard deviation from the mean.
10.The following represent scores on a 15 point aptitude test:8 10 15 12 14 13
(a)Find the sample mean and the sample variance for this data.
(b)Subtract 5 from every observation and
nd the sample mean and the sample variance
for the new data.
(c)What eff
ect, if any, does subtracting 5 from every observation have on the sample
mean and sample variance?
11.The following stem-and-leaf display shows the number of hours worked per week by a
sample of 25 students.
Stem Leaf
0 0 0 0 0 1 2
1 0 2 2 4 5 7 7 8
2 1 1 6 7
3 0 2 5 leaf unit = 1 hour (ones)
4 0 0 2 stem unit = 10 hours (tens)
5 1
We also know that sum of all the observation is 483 and sum of the square of
all observations is 14; 717.
(a)Find the mean of the sample.
(b)Find the standard deviation of the sample.
(c)Give the 5 number summary for this sample.
12. A NC consumer agency wishes to analyze the gas mileage of diff
erent car classes
(city cars and small hatchbacks, mid- to full size sedans, luxury cars, vans,
SUVs) for new cars. In order to gather data for this analysis, buyers of new cars in
North Carolina between January 1 and June 30, 2007 were contacted based on the
information obtained from NC car dealerships. Those buyers were then separated into
5 classes, based on the type of car they bought. Then, out of each class simple random
samples were selected. The chosen car buyers were contacted to see if they wished
to participate in the study. Upon agreement, their car was monitored for one week
and the following variables were recorded every day: gas used (in gallons), distance
driven (in miles), weight of car (in lbs), make and model. From these variables, the
agency computed the average gas mileage and weight of each car over one week. The
collected data was then used to compare the gas mileage between the car classes listed above.
(a)For the remainder of this question, we will concentrate on comparing
the classes “city cars and small hatchbacks” to “sedans”. The study contained 19 city cars and
small hatchbacks and their (sorted) gas mileage (in MPG) is given below:
25.05, 25.30, 29.82, 30.96, 32.31, 32.50, 32.62, 33.08, 33.24, 33.48,
33.76, 33.92, 35.86, 35.93, 36.93, 38.84, 39.73, 39.93, 40.02
Compute and give the Five Number Summary for the average gas mileage of these cars.
(b)The table below gives the Five Number Summary for the gas mileage of the 33 cars in the
“sedan” class.
Min Q1 Median Q3 Max
20.71 24.15 26.50 28.90 33.88
Use this information together with your result from the previous problem, to
construct side-by-side boxplots of the average gas mileage for “city cars and
small hatchbacks” and “sedans”. Be as exact as possible and do not forget to label your
boxplots properly. Also, briefly describe your conclusions from the side-by-side boxplot.
13.A sample of size 100 from a normal population has a mean of 110 and a standard
deviation of 10.0.Using the Empirical Rule(68-95-99.7 rule), about how many percent of
this sample will be above 130?
14.The distribution of heights of a large sample of adult US-females is approximately
normal with mean 64 inches, and standard deviation 3. Approximately what percent of
females are taller than 70 inches?
15.The histogram of times required to complete a math competency exam for all incoming
student in North Carolina in 2010 showed a normal distribution with a mean of 40 minutes
and a standard deviation of 5 minutes. Find the proportion of students needing only
30 minutes or less to fi
nish the exam.
16.Given a standard normal distribution, what can be said about the mean and standard deviation?
17.If the variability of a set of data is very small, then the sample variance may
be negative. Circle the correct answer! TRUE FALSE
18.The sample standard deviation is in the same units of measurement as the data.TRUE or FALSE
19.The total area under a density curve is … Circle the correct answer!
(a) equal to the number of individuals in the population.
(b) one.
(c) dependent on the mean and standard deviation of the distribution.
(d) zero.
(e) a measure of how close the distribution is to being normal.
20.The typical range of z-scores is between -3 and 3.
TRUE or FALSE
