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UNIT 3 REVIEW
True/False
Indicate whether the statement is true or false.
____
1. The mode is not affected by extreme values in a data set.
____
2. Because the denominator is n – 1, the sample standard deviation is adjusted to become a greater value than
when using the population standard deviation formula.
____
3. Whenever outliers are present in a set of data, they must be omitted.
____
4. Standard deviation shows how the data are clustered around the mean.
____
5. The interquartile range shows how the data are clustered around the median.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
6. The number of occurrences of a particular value is called the
a. range
c. tally
b. frequency
d. data
____
7. Which question(s) are meant to generate numeric data?
I. What is the fuel economy of your car?
II. How many cylinders does your car’s engine have?
III. Which manufacturer built your car?
a. only I
c. only III
b. only II
d. both I and II
____
8. Statistics is
a. the study of bar graphs, histograms, circle graphs and frequency polygons
b. the calculation of mean, median and mode
c. the gathering, organization, analysis and presentation of numerical information
d. a set of data
____
9. The number of patients treated in a dental office on Mondays was recorded for 11 weeks. What are the mean,
median, and mode for this set of data?
5, 17, 28, 28, 28, 15, 13, 18, 10, 16, 20
a. mean 17, median 18, mode 28
b. mean 18, median 17, mode 28
c. mean 16.5, median 18, mode 28
d. mean 28, median 17, mode 18
____ 10. Which of the following is not a characteristic of the median?
a. It is easy to define and easy to understand.
b. It is affected by the number of extreme values but not by their values.
c. It can be computed when data are grouped.
d. It does not exist for some sets of data.
Matching
Match these formulas to the terms below.
a.
d.
b.
e.
c.
f.
____ 11. population mean, 
____ 12. sample mean,
____ 13. population standard deviation, 
____ 14. sample standard deviation, s
____ 15. population variance, 
____ 16. sample variance, s2
Short Answer
17. What is wrong with the intervals in the following table?
Height (cm)
60–62
63–65
66–69
69–75
Frequency
6
18
44
10
18. When recommending five mutual funds for you to consider, a financial planner mentions that the typical
minimum investment is $2000 since the minimum investment amounts for the five funds are $500, $2000,
$2500, $25 000, and $2000, respectively. However, when you key these numbers into a calculator, you find
that the average minimum investment is, in fact, $6400. What accounts for this discrepancy?
19. A building maintenance company tracked the number of months that fluorescent tubes lasted in the different
offices in a building. Calculate the mean, median, and mode for this set of data.
8, 29, 22, 15, 10, 22, 12, 4, 22
20. The ages, in years, of a group of friends are listed below.
29, 33, 36, 48, 50, 51, 53, 53
a) Find the mean, median, and mode of the ages.
b) Explain what each of these measures tells you about this group of friends.
c) What do the relative values of the mean and median tell you about the group?
21. The mean of the values 9, 11, 13, 21, 24, 18, and d is 17. Find d.
22. Each child in a study of infantile autism was given a behavioural test and graded on a scale from 0 (no
symptoms) to 116 (maximum severity). The scores of the 21 children in the study were as follows.
27, 35, 65, 67, 47, 46, 63, 44, 34, 51, 17, 40, 41, 60, 24, 48, 29, 73, 60, 41, 47
Calculate the mean, the standard deviation, and the variance.
A consumer magazine evaluated 39 models of bathroom scales. The table below lists the prices for each
model (rounded to the nearest dollar).
Scale Model
EconoHealth A10
EconoHealth A12
EconoHealth B10
EconoHealth E10
EconoHealth Digital-10
EconoHealth E-20
EconoHealth E-30
HealthSkale 190
HealthSkale 210
HealthSkale 211
HealthSkale 290 Deluxe
HealthSkale 310
HealthSkale 1000
HealthSkale 1002
HydroXact 12573
HydroXact 12756
HydroXact 12856
Prowt P10A
Prowt Value
Prowt Value 2
Price ($)
50
50
50
28
65
40
50
22
32
30
79
50
23
20
35
24
25
120
35
35
Scale Model
Superskale 6400
Superskale 7200
Superskale 8000
Superskale 8280
SvelteChek 12300
SvelteChek 12400D
SvelteChek 12509
SvelteChek 12510
SvelteChek Fashion
SvelteChek Pro
SvelteChek Xtra
Weighbeter 550
Weighbeter 801D
Weighbeter 830
Weighbeter 835
Weighbeter 950
Weighbeter 2000
Weighbeter 2100
Weighbeter Basic
Price ($)
65
20
14
25
24
48
15
10
17
50
25
22
60
30
30
10
12
20
12
23. Find the median, first quartile, and third quartile for the prices of these bathroom scales.
24. Calculate the mean, standard deviation, and variance for the prices of these bathroom scales.
25. What is the z-score for the price of
a) the Weighbeter 801D scale?
b) the Weighbeter 830 scale?
26. What is the z-score for the price of
a) the EconoHealth E10 scale?
b) the HydroXact 12573 scale?
c) the Prowt P10A scale?
27. Find the range and the interquartile range for the prices of these bathroom scales.
Problem
28. The table summarizes data collected in a survey of owners of small trucks. Most owners reported their
distances rounded to the nearest 100 km.
Distance Travelled Annually (km)
5 000–6 999
7 000–8 999
9 000–10 999
11 000–12 999
13 000 –14 999
15 000–16 999
17 000–18 999
19 000–21 000
Number of Trucks
5
10
12
20
20
14
11
4
Estimate the mean distance these trucks were driven annually.
29. The table lists the approximate numbers of residents in 21 Canadian cities in 2002.
City
Calgary
Edmonton
Halifax
Hamilton
Kingston
Kitchener/Waterloo
Lethbridge
London
Ottawa
Regina
Saint John
a)
b)
c)
d)
e)
f)
Population
864 700
693 800
117 200
347 500
60 300
276 400
71 200
350 900
348 500
182 800
73 600
City
Saskatoon
Sault Sainte Marie
St. John's
Sudbury
Thunder Bay
Toronto
Vancouver
Victoria
Windsor
Winnipeg
Find the median, first quartile, and third quartile for these data.
Determine the range and interquartile range.
Calculate the mean, standard deviation, and variance.
What is the z-score for the population of Windsor?
What is the z-score for the population of Toronto?
Interpret the z-scores for Toronto and Windsor.
Population
72 500
193 600
97 500
99 200
122 500
2 571 700
534 600
76 600
213 100
635 200
UNIT 3 REVIEW
Answer Section
TRUE/FALSE
1. ANS:
OBJ:
KEY:
2. ANS:
OBJ:
KEY:
3. ANS:
OBJ:
KEY:
4. ANS:
OBJ:
KEY:
5. ANS:
OBJ:
KEY:
T
PTS: 1
Section 2.5
LOC: D1.1
mode | extreme values
T
PTS: 1
Section 2.6
LOC: D1.1
standard deviation
F
PTS: 1
Section 2.6
LOC: C1.2
outlier
T
PTS: 1
Section 2.6
LOC: D1.1
standard deviation | mean
T
PTS: 1
Section 2.6
LOC: D1.1
interquartile range | median
DIF: 1
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Organization of Data for Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Statistical Analysis
MULTIPLE CHOICE
6. ANS:
OBJ:
KEY:
7. ANS:
OBJ:
KEY:
8. ANS:
OBJ:
KEY:
9. ANS:
OBJ:
KEY:
10. ANS:
OBJ:
KEY:
B
PTS: 1
Section 2.1
LOC: C1.3
frequency
D
PTS: 1
Section 2.1
LOC: C1.3
type of data
C
PTS: 1
Section 2.1
LOC: C1.3
statistics
B
PTS: 1
Section 2.5
LOC: D1.1
mean | median | mode
D
PTS: 1
Section 2.5
LOC: D1.1
mean | median | mode
DIF: 1
REF: Knowledge & Understanding
TOP: Organization of Data for Analysis
E
PTS: 1
Section 2.6
LOC: D1.1
measures of dispersion
F
PTS: 1
Section 2.6
LOC: D1.1
measures of dispersion
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Organization of Data for Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Organization of Data for Analysis
DIF: 1
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
MATCHING
11. ANS:
OBJ:
KEY:
12. ANS:
OBJ:
KEY:
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
13. ANS:
OBJ:
KEY:
14. ANS:
OBJ:
KEY:
15. ANS:
OBJ:
KEY:
16. ANS:
OBJ:
KEY:
B
PTS: 1
Section 2.6
LOC: D1.1
measures of dispersion
A
PTS: 1
Section 2.6
LOC: D1.1
measures of dispersion
D
PTS: 1
Section 2.6
LOC: D1.1
measures of dispersion
C
PTS: 1
Section 2.6
LOC: D1.1
measures of dispersion
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
DIF: 2
REF: Knowledge & Understanding
TOP: Statistical Analysis
SHORT ANSWER
17. ANS:
The first two intervals should be joined at their endpoints, as should the last two, since height is a continuous
variable Also, the intervals have three different widths, so it is not possible to make direct comparisons of the
frequencies.
PTS: 1
DIF: 2
REF: Knowledge & Understanding
OBJ: Section 2.1
LOC: D1.3
TOP: Statistical Analysis
KEY: intervals
18. ANS:
You and the financial planner have interpreted the word typical differently. The planner was referring to the
mode of the minimum investment amounts, while you calculated the mean.
PTS: 1
DIF: 3
REF: Application
LOC: D1.5
TOP: Statistical Analysis
KEY: interpreting statistics | mean | median | mode
19. ANS:
mean 16, median 15, mode, 22
OBJ: Section 2.5
PTS: 1
DIF: 1
REF: Knowledge & Understanding
OBJ: Section 2.5
LOC: D1.1
TOP: Statistical Analysis
KEY: mean | median | mode
20. ANS:
a) mean 44.1, median 49, mode 53
b) The mean indicates that the arithmetic average of the ages is about 44. The median indicates that half of
the friends are under 49 and the other half are over 49. The mode indicates that 53 is the most common
age in the group, but this information is not significant since the group is so small.
c) Since the median is higher than the mean, the friends’ ages must be unevenly distributed.
PTS: 1
DIF: 3
REF: Application | Communication
OBJ: Section 2.5
LOC: D1.1 | D1.5 TOP: Statistical Analysis
KEY: interpreting statistics | mean | median | mode
21. ANS:
23
PTS: 1
DIF: 2
REF: Application OBJ: Section 2.5
LOC: D1.5
TOP: Statistical Analysis
KEY: mean
22. ANS:
Since the study is trying to determine the characteristics of the population of all autistic children, use the
formulas for calculating statistics for a sample.
= 45.7, s = 15.1, s2 = 229
PTS: 1
DIF: 2
REF: Application
LOC: D1.1
TOP: Statistical Analysis
23. ANS:
median $30, first quartile $20, third quartile $50
OBJ: Section 2.6
KEY: measures of dispersion
PTS: 1
DIF: 2
REF: Application OBJ: Section 2.6
LOC: D1.2
TOP: Statistical Analysis
KEY: median | quartiles
24. ANS:
The 39 scales in the survey can be considered a sample of the population of all the different bathroom scales
on the market. Therefore, use the formulas for calculating statistics for a sample.
= $35.18, s = $22.02, s2 = 485
PTS: 1
LOC: D1.1
25. ANS:
a) 1.13
b) –0.24
DIF: 2
REF: Application
TOP: Statistical Analysis
OBJ: Section 2.6
KEY: measures of dispersion
PTS: 1
LOC: D1.2
26. ANS:
a) –0.33
b) –0.0082
c) 3.85
DIF: 3
REF: Application
TOP: Statistical Analysis
OBJ: Section 2.6
KEY: z-score
PTS: 1
DIF: 3
REF: Application
LOC: D1.2
TOP: Statistical Analysis
27. ANS:
range $110, interquartile range $30
OBJ: Section 2.6
KEY: z-score
PTS: 1
LOC: D1.1
PROBLEM
28. ANS:
DIF: 3
REF: Application
TOP: Statistical Analysis
OBJ: Section 2.6
KEY: measures of dispersion
These trucks were driven a mean distance of about 13 000 km annually.
PTS: 1
DIF: 2
REF: Application OBJ: Section 2.5
LOC: D1.1
TOP: Statistical Analysis
KEY: mean
29. ANS:
a) Since there are 21 cities listed, the median is the 11th greatest value in the set of data: 193 600. The first
quartile is the midpoint between the fifth and sixth least values, so Q1 = 97 500. Similarly, the third
quartile is the midpoint between the fifth and sixth greatest values, so Q3 = 350 900.
The median and quartiles can be calculated with a graphing calculator by entering the data into a list and
then using the 1-Var Stats function from the STAT CALC menu. In a spreadsheet, you can use the
MEDIAN and QUARTILE functions.
b) The range is the greatest value minus the least one: 2 571 700 – 60 300 = 2 511 400. The interquartile
range is Q3 – Q1 = 253 400.
c) The 21 cities can be considered a sample of all the cities in Canada. Therefore, use the sample version of
the formulas for the mean, standard deviation, and variance. On a graphing calculator, the 1-VAR Stats
function will calculate both and s. In Microsoft® Excel, you can use the AVERAGE, STDEV, and
VAR functions to calculate , s, and s2, respectively. In Corel® Quattro® Pro, use @AVG, @STDS, and
@VARS. The resulting values are = 381 114, s = 552 863, and s2 = 3.056 575  1011.
d) For Windsor,
e) For Toronto,
f) Windsor’s population is slightly less than the mean population, whereas Toronto’s is significantly greater
than the mean.
PTS: 1
DIF: 4
REF: Application OBJ: Section 2.6
LOC: D1.1 | D1.2 | D1.5
TOP: Statistical Analysis
KEY: measures of dispersion | variance | standard deviation