MCQ

Multiple Choice QuestionsDescriptive 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 seniorstatistician/owner $270,000. The number of employees earning less thanthe mean salary is:

(a) 0

(b) 4

(c) 5

(d) 6

(e) 7

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

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

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 theprocess of negotiating with the team owners for higher minimum salariesand more fringe benefits. At the time of the negotiations, most of themajor league baseball players had salaries in the $100,000 ů $150,000 ayear range. However, there were a handful of players who, via the freeagent system, earned nearly three million dollars per year. Which measureof central tendency of players’ salaries, the mean or the median, might theplayers 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 thesame.

(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 followingweight 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 SASappears below:

QUANTILES(DEF=4) EXTREMESN 13 SUM WGTS 13 100% MAX 392 99% 392 LOW HIGHMEAN 220.231 SUM 2863 75% Q3 234 95% 392 161 225STD DEV 58.5721 VAR 3430.69 50% MED 221 90% 330 168 232SKEW 2.21591 KURT 6.61979 25% Q1 174 10% 163 169 236USS 671689 CSS 41168.3 0% MIN 161 5% 161 179 239CV 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 manyplaces where excess irrigation is causing salt to rise to the surface. Inorder to determine baseline yields, a sample of 24 fields was selected, andthe biomass of grasses in a standard sized plot was measured (kg). Theoutput from SAS appears below:

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


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 thesame 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 shapewould a histogram of the data set have?

(a) The mean would be smaller than the median and the histogram wouldbe skewed with a long left tail.

(b) The mean would be larger than the median and the histogram wouldbe skewed with a long right tail.

(c) The mean would be larger than the median and the histogram wouldbe skewed with a long left tail.

(d) The mean would be smaller than the median and the histogram wouldbe skewed with a long right tail.

(e) The mean would be equal to the median and the histogram would besymmetrical.

10. In measuring the centre of the data from a skewed distribution, the medianwould 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 observationsand this gives too high an indication of the centre

(c) the median is less than the mean and smaller numbers are alwaysappropriate for the centre

(d) the mean measures the spread in the data

(e) the median measures the arithmetic average of the data excludingoutliers.

11. In general, which of the following statements is FALSE?

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


(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 thesample mean.

(d) The sample standard deviation is a measure of central tendencyaround the median.

(e) If a distribution is symmetric, then the mean will be equal to themedian.

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

Rainfall Number(in inches) of years2.0 - 4.0 34.0 - 6.0 66.0 - 8.0 88.0 - 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 newproduct on the market. A random sample of 25 items of the product wastaken and the weights (in grams) of these items were classified as follows:

Class Limits Frequency74 - 77 377 - 80 680 - 83 983 - 86 386 - 89 4

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

(a) 83.00

(b) 75.00

(c) 83.75


(d) 18.75(e) 84.50

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

Ages Frequency10 - 20 420 - 30 630 - 40 1240 - 50 1050 - 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 givenbelow:

Weekly wages Frequency50.00 - 75.00 1075.00 - 100.00 15

100.00 - 125.00 60125.00 - 150.00 40150.00 - 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 thanor equal to Cum. rel. freq.

5.0 0.2310.0 0.3415.0 0.4120.0 1.00


If this distribution is based on 800 observations, then the frequency in thesecond 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 Frequency0 - 5 85 -10 210-15 615-20 820-25 525-30 530-35 035-40 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) 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 45samples of water downstream from the treated sewage outlet and measuresthe number of coliform bacteria present. A summary table is as follows:

Number of Number ofBacteria Samples

20-30 530-40 2040-50 1550-60 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 50samples of water downstream from the treated sewage outlet and measuresthe number of coliform bacteria present. A summary table is as follows:

Number of Number ofBacteria Samples50-60 560-70 2070-80 1080-90 15

The mean number of bacteria per sample is:

(a) 70

(b) 71

(c) 72

(d) 76

(e) 65


22. Using the same data as in the previous question, the 75th percentile isapproximately:

(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 waserroneously recorded as “30” actually had a value of “35”. If we make thiscorrection 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 classwere 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 willchange 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 anda mode of $80.00. Which of the following is a possible value for the meanof distribution?

(a) $86

(b) $91

(c) $64


(d) $75

(e) None of these

26. Earthquake intensities are measured using a device called a seismographwhich is designed to be most sensitive for earthquakes with intensitiesbetween 4.0 and 9.0 on the open-ended Richter scale. Measurements ofnine 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 aH indicates that the earthquake had an intensity above 9.0. The medianearthquake 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 seismographwhich is designed to be most sensitive for earthquakes with intensitiesbetween 4.0 and 9.0 on the open-ended Richter scale Measurements of tenearthquakes gave the following readings:

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 Hindicates that the earthquake had an intensity above 9.0. One measure ofcentral 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 asbdl, i.e., below detection limit. The following are the measurements ofthe amount of lead in a series of water samples taken from inner cityhouseholds (ppm).


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 somevalues are unknown.

29. A clothing and textiles student is trying to assess the effect of a jacket’sdesign on the time it takes preschool children to put the jacket on. In apretest, she timed 7 children as they put on her prototype jacket. Thetimes (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 followingwould be the best value to use as the “typical” time required to put on thejacket?

(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.


(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 Bsample size 45 30sample mean 1000 lbs 800 lbssample 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 standarddeviation is larger.

(b) Group A is relatively less variable than Group B because Group A’scoefficient of variation (the ratio of the standard deviation to themean) is smaller

(c) Group A is less variable than Group B because the std deviation peranimal is smaller.

(d) Group A is relatively more variable than Group B because the samplemean is larger.

(e) Group A is more variable than Group B because the sample size islarger.

32. “Normal” body temperature varies by time of day. A series of readingswas taken of the body temperature of a subject. The mean reading wasfound to be 36.5řC with a standard deviation of 0.3řC. When convertedto 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 astandard deviation of 2 g. After completing the weighing, she finds thatthe 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 ismean and standard deviation after correcting for the error in the scale?[Hint: recall that the mean measures central tendency and the standarddeviation measures spread.]


(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 sufferingfrom a particular disease. From patient records, the mean was computedas 156 cm, and standard deviation as 5 cm. Further investigation revealsthat 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 onmetres. 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 anindustrial basin and the amount of acidity (pH level) was measured. Themean 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 foundto be in error. The error can be corrected by adding 0.1 pH units to all ofthe values and then multiply the result by 1.2. The mean and standarddeviation 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.


37. An experiment was conducted where a person’s heart rate was measured4 times in the space of 10 minutes. This was repeated on a sample of 20people. 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 inheart rates among different people.

(c) The variation among subjects was larger than the variation withinsubjects.

(d) The variation in heart rates based on measurements taken for 30seconds 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 ratescomputed from the 30 second measurement periods.

38. Here is a summary graph of complex carbohyrates for each of the threefibre groups in the cereal dataset.

Which of the following is NOT correct?

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


(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 complexcarbohydrates per serving.

(d) The average amount of complex carbohydrates per serving for thehigh fibre group appears to be much smaller than the other twogroups.

(e) About 25% of the medium fibre cereals have less than 10 g of complexcarbohydrates.

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 withoutrepeats. 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 thenumbers 1231, 1235, 1237, 1239.

(c) The numbers 1, 5, 6, 10 has a larger standard deviation than thenumbers 1231, 1232, 1233, 1234.

(d) The numbers 1, 2, 9, 10 has the same standard standard deviationas the numbers 1231, 1232, 1239, 1240.

(e) The numbers 1236, 1237, 1238, 1239 has the smallest possible stan-dard deviation.


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