# Multiple Choice Questions Descriptive Statistics

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```					         Multiple Choice Questions
Descriptive Statistics - Summary Statistics

1. Last year a small statistical consulting company paid each of its ﬁve sta-
tistical clerks \$22,000, two statistical analysts \$50,000 each, and the senior
statistician/owner \$270,000. The number of employees earning less than
the mean salary is:

(a) 0
(b) 4
(c) 5
(d) 6
(e) 7

2. The following table represents the relative frequency of accidents per day
in a city.

Accidents         0          1           2          3       4 or more
Relative         0.55       0.20        0.10       0.15       0
Frequency

Which of the following statements are true?

I.   The mean and modal number of accidents are equal.
II. The mean and median number of accidents are equal.
III. The median and modal number of accidents are equal.

(a) I only
(b) II only
(c) III only
(d) I, II and III
(e) I, II

1
3. During the past few months, major league baseball players were in the
process of negotiating with the team owners for higher minimum salaries
and more fringe beneﬁts. At the time of the negotiations, most of the
major league baseball players had salaries in the \$100,000 ů \$150,000 a
year range. However, there were a handful of players who, via the free
agent system, earned nearly three million dollars per year. Which measure
of central tendency of players’ salaries, the mean or the median, might the
players have used in an attempt to convince the team owners that they
(the players) were deserving of higher salaries and more fringe beneﬁts?

(a) Not enough information is given to answer the question.
(b) Either one, because all measures of central tendency are basically the
same.
(c) Mean.
(d) Median.
(e) Both the mean and the median.

4. A ﬁnancial analyst’s sample of six companies’ book value were

\$25,     \$7,      \$22,    \$33,   \$18,   \$15.

The sample mean and sample standard deviation are (approximately):

(a) 20 and 79.2 respectively
(b) 20 and 8.9 respectively.
(c) 120 and 79.2 respectively.
(d) 20 and 8.2 respectively.
(e) 120 and 8.9 respectively.

5. A sample of underweight babies was fed a special diet and the following
weight gains (lbs) were observed at the end of three month.

6.7             2.7      2.5     3.6     3.4   4.1     4.8       5.9     8.3

The mean and standard deviation are:

(a) 4.67, 3.82
(b) 3.82, 4.67
(c) 4.67, 1.95
(d) 1.95, 4.67
(e) 4.67, 1.84

c 2006 Carl James Schwarz                     2
6. The eﬀect of acid rain upon the yield of crops is of concern in many places.
In order to determine baseline yields, a sample of 13 ﬁelds was selected,
and the yield of barley (g/400 m2 ) was determined. The output from SAS
appears below:

QUANTILES(DEF=4)             EXTREMES
N                 13   SUM WGTS      13   100%   MAX 392     99%      392     LOW HIGH
MEAN         220.231   SUM         2863    75%   Q3   234    95%      392     161 225
STD DEV      58.5721   VAR     3430.69     50%   MED 221     90%      330     168 232
SKEW         2.21591   KURT    6.61979     25%   Q1   174    10%      163     169 236
USS           671689   CSS      41168.3     0%   MIN 161      5%      161     179 239
CV           26.5958   STD MEAN 16.245                        1%      161     205 392

The mean, standard deviation, median, and the highest value are:
(a) 220.231 3430.60 50% 225
(b) 220.231 16.245 221 225
(c) 220.231 58.5721 50% 392
(d) 220.231 58.5721 221 392
(e) 220.231 58.5721 234 392
7. The eﬀect of salinity upon the growth of grasses is of concern in many
places where excess irrigation is causing salt to rise to the surface. In
order to determine baseline yields, a sample of 24 ﬁelds was selected, and
the biomass of grasses in a standard sized plot was measured (kg). The
output from SAS appears below:

QUANTILES(DEF=4)               EXTREMES
N           24 SUM WGTS   24  100%         MAX 22.6     99% 22.6              LOW HIGH
MEAN      9.09 SUM     218.3   75%         Q3 11.45     95% 22.52             0.7 15.1
STD DEV 6.64 VARIANCE 44.0     50%         MED 8.15     90% 21.8                1 19.8
SKEWNE 0.924 KURTO -0.0209     25%         Q1 3.775     10%   1.6             2.2 21.3
USS      2998 CSS    1012.73    0%         MIN    0.7    5% 0.77              2.2 22.3
CV         72 STD MEAN 1.35                              1%   0.7             2.8 22.6
T:MEAN=0 6.7153 PROb>|T| 0.0001                   RANGE         21.9
SGN RANK      150 PROb>|S| 0.0001                 Q3-Q1        7.675

The mean, standard deviation, tenth percentile, and the highest value are:
(a) 9.09 44.0 10% 22.6
(b) 9.09 6.64 1.6 15.1
(c) 9.09 6.64 21.8 15.1
(d) 9.09 6.64 1.6 22.6
(e) 9.09 1.35 21.8 15.1

c 2006 Carl James Schwarz                3
8. The heights in centimeters of 5 students are:

165, 175, 176, 159, 170.

The sample median and sample mean are respectively:
(a) 170, 169
(b) 170, 170
(c) 169, 170
(d) 176, 169
(e) 176, 176
9. If most of the measurements in a large data set are of approximately the
same magnitude except for a few measurements that are quite a bit larger,
how would the mean and median of the data set compare and what shape
would a histogram of the data set have?

(a) The mean would be smaller than the median and the histogram would
be skewed with a long left tail.
(b) The mean would be larger than the median and the histogram would
be skewed with a long right tail.
(c) The mean would be larger than the median and the histogram would
be skewed with a long left tail.
(d) The mean would be smaller than the median and the histogram would
be skewed with a long right tail.
(e) The mean would be equal to the median and the histogram would be
symmetrical.

10. In measuring the centre of the data from a skewed distribution, the median
would be preferred over the mean for most purposes because:
(a) the median is the most frequent number while the mean is most likely
(b) the mean may be too heavily inﬂuenced by the larger observations
and this gives too high an indication of the centre
(c) the median is less than the mean and smaller numbers are always
appropriate for the centre
(d) the mean measures the spread in the data
(e) the median measures the arithmetic average of the data excluding
outliers.
11. In general, which of the following statements is FALSE?

(a) The sample mean is more sensitive to extreme values than the me-
dian.

c 2006 Carl James Schwarz               4
(b) The sample range is more sensitive to extreme values than the stan-
dard deviation.
(c) The sample standard deviation is a measure of spread around the
sample mean.
(d) The sample standard deviation is a measure of central tendency
around the median.
(e) If a distribution is symmetric, then the mean will be equal to the
median.

12. The frequency distribution of the amount of rainfall in December in a
certain region for a period of 30 years is given below:

Rainfall           Number
(in inches)       of years
2.0 - 4.0           3
4.0 - 6.0           6
6.0 - 8.0           8
8.0 - 10.0          8
10.0 - 12.0          5

The mean amount of rainfall in inches is:

(a) 7.30
(b) 7.25
(c) 7.40
(d) 8.40
(e) 6.50

13. A consumer aﬀairs agency wants to check the average weight of a new
product on the market. A random sample of 25 items of the product was
taken and the weights (in grams) of these items were classiﬁed as follows:

Class Limits   Frequency
74 - 77             3
77 - 80             6
80 - 83             9
83 - 86             3
86 - 89             4

The 3rd quartile of the weight in this sample is equal to:

(a) 83.00
(b) 75.00
(c) 83.75

c 2006 Carl James Schwarz                  5
(d) 18.75
(e) 84.50

14. A random sample of 40 smoking people is classiﬁed in the following table:

Ages          Frequency
10 - 20                4
20 - 30                6
30 - 40               12
40 - 50               10
50 - 60                8
Total               40

The mean age of this group of people.
(a)   4.5
(b)   8.0
(c)   34.5
(d)   38.0
(e)   1520.0
15. A frequency distribution of weekly wages for a group of employees is given
below:

Weekly   wages          Frequency
50.00   - 75.00           10
75.00   - 100.00          15
100.00   - 125.00          60
125.00   - 150.00          40
150.00   - 175.00          10

The mean for this group is:

(a)   \$112.50
(b)   \$125.00
(c)   \$105.41
(d)   \$117.13
(e)   \$118.50

16. Consider the following cumulative relative frequency distribution:

Less than
or equal to      Cum. rel. freq.
5.0             0.23
10.0             0.34
15.0             0.41
20.0             1.00

c 2006 Carl James Schwarz                  6
If this distribution is based on 800 observations, then the frequency in the
second interval is:

(a) 34
(b) 272
(c) 80
(d) 88
(e) 456

The following information will be used in the next three ques-
tions.
A sample of 35 observations were classiﬁed as follows:

Class        Frequency
0 - 5          8
5 -10          2
10-15          6
15-20          8
20-25          5
25-30          5
30-35          0
35-40          1

17. The class mark of the third class is:
(a) 10.0
(b) 12.5
(c) 15.0
(d) 7.5
(e) 17.5
18. The sample mean of the above grouped data is:

(a) 14.89
(b) 14.23
(c) 15.35
(d) 15.11
(e) 14.74

19. The 80th percentile of the above grouped data is:

(a) 27
(b) 22

c 2006 Carl James Schwarz                7
(c) 19
(d) 23
(e) 24

20. Recently, the City of Winnipeg has been criticized for its excessive dis-
charges of untreated sewage into the Red River. A microbiologist take 45
samples of water downstream from the treated sewage outlet and measures
the number of coliform bacteria present. A summary table is as follows:

Number of       Number of
Bacteria        Samples
20-30              5
30-40             20
40-50             15
50-60              5

The 80th percentile is approximately:

(a) 45
(b) 47
(c) 80
(d) 48
(e) 36

21. Recently, the City of Winnipeg has been criticized for its excessive dis-
charges of untreated sewage into the Red River. A microbiologist take 50
samples of water downstream from the treated sewage outlet and measures
the number of coliform bacteria present. A summary table is as follows:

Number of      Number of
Bacteria       Samples
50-60             5
60-70            20
70-80            10
80-90            15

The mean number of bacteria per sample is:

(a) 70
(b) 71
(c) 72
(d) 76
(e) 65

c 2006 Carl James Schwarz               8
22. Using the same data as in the previous question, the 75th percentile is
approximately:

(a) 76.5
(b) 77.5
(c) 75.0
(d) 78.5
(e) 78.0

23. A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet.
Unfortunately, it has just been discovered that an observation which was
erroneously recorded as “30” actually had a value of “35”. If we make this
correction to the data, then:

(a) the mean remains the same, but the median is increased
(b) the mean and median remain the same
(c) the median remains the same, but the mean is increased
(d) the mean and median are both increased
(e) we do not know how the mean and median are aﬀected without fur-
ther calculations; but the variance is increased.

24. The term test scores of 15 students enrolled in a Business Statistics class
were recorded in ascending order as follows:

4, 7, 7, 9, 10, 11, 13, 15, 15, 15, 17, 17, 19, 19, 20

After calculating the mean, median, and mode, an error is discovered:
one of the 15’s is really a 17. The measures of central tendency which will
change are:

(a) the mean only
(b) the mode only
(c) the median only
(d) the mean and mode
(e) all three measures

25. Suppose a frequency distribution is skewed with a median of \$75.00 and
a mode of \$80.00. Which of the following is a possible value for the mean
of distribution?

(a) \$86
(b) \$91
(c) \$64

c 2006 Carl James Schwarz               9
(d) \$75
(e) None of these

26. Earthquake intensities are measured using a device called a seismograph
which is designed to be most sensitive for earthquakes with intensities
between 4.0 and 9.0 on the open-ended Richter scale. Measurements of
nine earthquakes gave the following readings:

4.5          L   5.5   H   8.7   8.9   6.0   H   5.2

where L indicates that the earthquake had an intensity below 4.0 and a
H indicates that the earthquake had an intensity above 9.0. The median
earthquake intensity of the sample is:

(a) Cannot be computed because all of the values are not known
(b) 8.70
(c) 5.75
(d) 6.00
(e) 6.47

27. Earthquake intensities are measured using a device called a seismograph
which is designed to be most sensitive for earthquakes with intensities
between 4.0 and 9.0 on the open-ended Richter scale Measurements of ten

4.5          L   5.5   H   8.7   8.9   6.0   H   5.2   7.2

where L indicates that the earthquake had an intensity below 4.0 and a H
indicates that the earthquake had an intensity above 9.0. One measure of
central tendancy is the x% trimmed mean computed after trimming x%
of the upper values and x% of the bottom values. The value of the 20%
trimmed mean is:

(a) Cannot be computed because all of the values are not known
(b) 6.00
(c) 6.60
(d) 6.92
(e) 6.57

28. When testing water for chemical impurities, results are often reported as
bdl, i.e., below detection limit. The following are the measurements of
the amount of lead in a series of water samples taken from inner city
households (ppm).

c 2006 Carl James Schwarz                  10
5, 7, 12, bdl, 10, 8, bdl, 20, 6.

Which of the following is correct?
(a) The mean lead level in the water is about 10 ppm.
(b) The mean lead level in the water is about 8 ppm.
(c) The median lead level in the water is 7 ppm.
(d) The median lead level in the water is 8 ppm.
(e) Neither the mean nor the median can be computed because some
values are unknown.
29. A clothing and textiles student is trying to assess the eﬀect of a jacket’s
design on the time it takes preschool children to put the jacket on. In a
pretest, she timed 7 children as they put on her prototype jacket. The
times (in seconds) are provided below.

n            n   65   43        n    119       39

The n’s represent children who had not put the jacket on after 120 seconds
(in which case the children were allowed to stop). Which of the following
would be the best value to use as the “typical” time required to put on the
jacket?

(a) The median time, which was 43 seconds.
(b) The mean time, which was 66 seconds.
(c) The median time, which was 52 seconds. ok
(d) The median time, which was 119 seconds. ok
(e) The missing times (the n’s) mean we can’t calculate any useful mea-
sures of central tendency.

30. For the following histogram, what is the proper ordering of the mean,
median, and mode? Note that the graph is NOT numerically precise -
only the relative positions are important.

c 2006 Carl James Schwarz                 11
(a) I = mean II = median III = mode
(b) I =mode II = median III = mean
(c) I = median II = mean III = mode
(d) I = mode II = mean III = median
(e) I = mean II = mode III = median

31. The following statistics were collected on two groups of cattle

Group A              Group B
sample size             45                    30
sample mean          1000 lbs                800 lbs
sample std. dev        80 lbs                 70 lbs

Which of the following statements is correct?
(a) Group A is less variable than Group B because Group A’s standard
deviation is larger.
(b) Group A is relatively less variable than Group B because Group A’s
coeﬃcient of variation (the ratio of the standard deviation to the
mean) is smaller
(c) Group A is less variable than Group B because the std deviation per
animal is smaller.
(d) Group A is relatively more variable than Group B because the sample
mean is larger.
(e) Group A is more variable than Group B because the sample size is
larger.
32. “Normal” body temperature varies by time of day. A series of readings
was taken of the body temperature of a subject. The mean reading was
found to be 36.5řC with a standard deviation of 0.3řC. When converted
to řF, the mean and standard deviation are: (řF = řC(1.8) + 32).
(a) 97.7, 32
(b) 97.7, 0.30
(c) 97.7, 0.54
(d) 97.7, 0.97
(e) 97.7, 1.80
33. A scientist is weighing each of 30 ﬁsh. She obtains a mean of 30 g and a
standard deviation of 2 g. After completing the weighing, she ﬁnds that
the scale was misaligned, and always under reported every weight by 2 g,
i.e. a ﬁsh that really weighed 26 g was reported to weigh 24 g. What is
mean and standard deviation after correcting for the error in the scale?
[Hint: recall that the mean measures central tendency and the standard

c 2006 Carl James Schwarz              12
(a) 28 g, 2 g
(b) 30 g, 4 g
(c) 32 g, 2 g
(d) 32 g, 4 g
(e) 28 g, 4 g
34. A researcher wishes to calculate the average height of patients suﬀering
from a particular disease. From patient records, the mean was computed
as 156 cm, and standard deviation as 5 cm. Further investigation reveals
that the scale was misaligned, and that all reading are 2 cm too large,
e.g., a patient whose height is really 180 cm was measured as 182 cm.
Furthermore, the researcher would like to work with statistics based on
metres. The correct mean and standard deviation are:
(a) 1.56m, .05m
(b) 1.54m, .05m
(c) 1.56m, .03m
(d) 1.58m, .05m
(e) 1.58m, .07m
35. Rainwater was collected in water collectors at thirty diﬀerent sites near an
industrial basin and the amount of acidity (pH level) was measured. The
mean and standard deviation of the values are 4.60 and 1.10 respectively.
When the pH meter was recalibrated back at the laboratory, it was found
to be in error. The error can be corrected by adding 0.1 pH units to all of
the values and then multiply the result by 1.2. The mean and standard
deviation of the corrected pH measurements are:

(a) 5.64, 1,44
(b) 5.64, 1.32
(c) 5.40, 1.44
(d) 5.40, 1.32
(e) 5.64, 1.20

36. Which of the following statements is NOT true?
(a) In a symmetric distribution, the mean and the median are equal.
(b) The ﬁrst quartile is equal to the twenty-ﬁfth percentile.
(c) In a symmetric distribution, the median is halfway between the ﬁrst
and the third quartiles.
(d) The median is always greater than the mean.
(e) The range is the diﬀerence between the largest and the smallest ob-
servations in the data set.

c 2006 Carl James Schwarz               13
37. An experiment was conducted where a person’s heart rate was measured
4 times in the space of 10 minutes. This was repeated on a sample of 20
people. Which of the following is not correct?
(a) The standard deviation within subjects refers to the repeated mea-
surements of a single person’s heart rate.
(b) The standard deviation among subjects refers to the variation in
heart rates among diﬀerent people.
(c) The variation among subjects was larger than the variation within
subjects.
(d) The variation in heart rates based on measurements taken for 30
seconds was larger than the variation of heart rates based on mea-
surements taken for 15 seconds.
(e) The average of the heart rate computed from the 15 seconds mea-
suring period was about the same as the average of the heart rates
computed from the 30 second measurement periods.
38. Here is a summary graph of complex carbohyrates for each of the three
ﬁbre groups in the cereal dataset.

Which of the following is NOT correct?

(a) The low ﬁbre group is more variable than the medium ﬁbre group
because the central box is larger.

c 2006 Carl James Schwarz             14
(b) About 25% of low ﬁbre cereals have less than 12 g of complex carbo-
hydrates per serving.
(c) About 50% of medium ﬁbre cereals have more than 15 g of complex
carbohydrates per serving.
(d) The average amount of complex carbohydrates per serving for the
high ﬁbre group appears to be much smaller than the other two
groups.
(e) About 25% of the medium ﬁbre cereals have less than 10 g of complex
carbohydrates.

39. You are allowed to choose four whole numbers from 1 to 10 (inclusive,
without repeats). Which of the following is FALSE?
(a)   The numbers 4, 5, 6, 7 have the smallest possible standard deviation.
(b)   The numbers 1, 2, 3, 4 have the smallest possible standard deviation.
(c)   The numbers 1, 5, 6, 10 have the largest possible standard deviation.
(d)   The numbers 1, 2, 9, 10 have the largest possible standard deviation.
(e)   The numbers 7, 8, 9, 10 have the smallest possible standard deviation.
40. Which of the following is FALSE:
(a) The numbers 3, 3, 3 have a standard deviation of 0.
(b) The numbers 3, 4, 5 have the same standard deviation as 1003, 1004,
1005.
(c) The standard deviation is a measure of spread around the centre of
the data.
(d) The numbers 1, 5, 9 have a smaller standard deviation than 101, 105,
109.
(e) The standard deviation can only be computed for interval or ratio
scaled data.
41. You are allowed to choose any four integers, without limits but without
repeats. Which of the following is FALSE?
(a) The numbers 4, 5, 6, 7 has the same standard deviation as the num-
bers 1231, 1232, 1233, 1234.
(b) The numbers 1, 5, 7, 9 has a smaller standard deviation than the
numbers 1231, 1235, 1237, 1239.
(c) The numbers 1, 5, 6, 10 has a larger standard deviation than the
numbers 1231, 1232, 1233, 1234.
(d) The numbers 1, 2, 9, 10 has the same standard standard deviation
as the numbers 1231, 1232, 1239, 1240.
(e) The numbers 1236, 1237, 1238, 1239 has the smallest possible stan-
dard deviation.

c 2006 Carl James Schwarz                 15

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