Loyola MBA Program
Instructor
Nate Straight, Loyola M.B.A. ‘08
• College of Business’ Director of
Assessment; Business Statistics &
Quantitative Methods Instructor
• GMAT Score of 760, 99th percentile
• natestraight@business.loyno.edu
Materials
www.loyno.edu/~nmstraig/GMAT
Structure and Scoring
Test Structure
4 sections, taken in this order:
Analytical Writing – 30 minutes
Integrated Reasoning – 30 minutes
Math / Quantitative – 75 minutes
Verbal Reasoning – 75 minutes
Test Structure
Analytical Writing (30 mins.):
1 essay requiring analysis of the
reasoning behind a presented
argument and communication
of a critique of the argument
Test Structure
Integrated Reasoning (30 mins.):
12 multiple-choice questions
Interpretation of graphics / tables
Reasoning from multiple sources
Multiple-step/two-part analysis
Test Structure
Math / Quantitative (75 mins.):
37 multiple-choice questions
50% problem-solving
50% “data sufficiency”
Test Structure
Verbal Reasoning (75 mins.):
41 multiple-choice questions
40% sentence correction
30% reading comprehension
30% critical reasoning
GMAT Scoring
Scores use the following ranges:
Analytical Writing – 0 to 6
Integrated Reasoning – 1 to 8
Math / Quantitative – 0 to 60
Verbal Reasoning – 0 to 60
Total Score – 200 to 800
GMAT Scoring
Your GMAT Score Report:
Math
%
Verb
%
Total
%
AWA
%
IR
%
36
42
30
56
550
48
4.5
38
6
79
Your total score ↑ depends only on your
math and your verbal reasoning scores.
Loyola’s average GMAT score is a 520
Improving your Score
More Test Structure
The GMAT is taken on a computer,
one question at a time, and you can
not skip or come back to questions.
The math / quantitative and verbal
sections are “computer-adaptive”.
Computer-Adaptive
The math and verbal sections start
with medium-difficulty questions
and ramp up or down the difficulty
based on your prior performance.
Your score increases with difficulty.
Computer-Adaptive
The goal of adaptive scoring is to
gradually hone in on your level of
ability, which determines your score.
Earlier questions identify your general
ability and have a large impact on your
score. Later questions are ‘fine-tuning’.
Computer-Adaptive
800
700
600
500
400
300
200
Q1
Q2
Q3
Q4
…
Q35
Q36
Q37
Computer-Adaptive
Strategies for adaptive testing:
Early questions are very important;
spend your time getting them right.
Especially early, difficult questions
can dramatically improve your score.
Plan to never miss an easy question.
Computer-Adaptive
Strategies for adaptive testing:
Unanswered questions at the end
will decrease your score; even if not
much individually, they will add up.
If you are running out of time, use
process of elimination, then guess.
Computer-Adaptive
Strategies for adaptive testing:
Early, easy-sounding questions will
have easy answers; later, as difficulty
rises these “easy” answers are a trap.
If an answer seems obviously right,
rethink it carefully before choosing it.
Process of Elimination
“18 percent of American corn is grown in
Iowa. If the total amount of corn grown in
America is 12 billion bushels, how many of
those bushels are grown outside of Iowa?”
A. 2.2 billion
D. 11.8 billion
B. 6 billion
E. 13.2 billion
C. 9.8 billion
Process of Elimination
“A company’s sales increased 10% from
2012 to 2013, and then 20% from 2013 to
2014. By approximately what percent did
sales increase overall from 2012 to 2014?”
A. 20%
D. 32%
B. 24%
E. 40%
C. 30%
Process of Elimination
“An MBA student took 2 classes in Fall with
an average grade of 80, then 3 classes in the
Spring with an average grade of 90. What
is the student’s average grade for the year?”
A. 83.3
D. 86
B. 85
E. 88
C. 85.5
General Strategies
There is no substitute for content
knowledge. Process of elimination
and other strategies are a last resort.
It will always be quicker to solve the
problem directly than to work through
5 answers trying to find the right one.
General Strategies
There is also no substitute for knowing
your own ability level and limitations.
You should spend as little test time as
possible trying to jog your faded highschool algebra or grammar memory
bank in search of long-lost knowledge.
General Strategies
The first 15-20 seconds after reading a
problem should be spent considering
a) whether you know how to solve the
problem; b) if not, whether you can
figure out how to identify the answer.
Be fully honest in this self-reflection.
General Strategies
If you know that you do not know how
to solve a problem, and cannot even
come up with a way to find an answer,
just take your best guess and move on.
Staring at the problem will not make
you understand it; it only wastes time.
General Strategies
Practice exams are more helpful than
random study. There are 2 full-length
tests available at: http://www.mba.com/us/
the-gmat-exam/prepare-for-the-gmat-exam.aspx
Take the first test, review in detail all
the content you missed, then re-take.
Overview and Strategies
Math Overview
2 types of questions:
50% problem-solving
50% “data sufficiency”
A calculator is neither provided nor
allowed for the math section. Do not
use one while you study for the exam.
Math Overview
Problem-solving content:
Order of operations
Properties / types of numbers
Fractions, ratios, and proportions
Operations using fractions / decimals
Percentages and percent change
Math Overview
Problem-solving content:
Probability and permutations
Mean, median, and mode
Range and standard deviation
Exponents and square roots
Operations using exponents
Math Overview
Problem-solving content:
Algebra for “word problems”
“Solving for X” / plugging-in
Solving systems of equations
Using algebraic functions
Algebraic factorization
Math Overview
Problem-solving content:
Distance/rate/time problems
Work/rate/time problems
Geometry: Angles and area
Solids: Volume and surface area
Lines: Slope, intercept, and areas
Math Overview
Data sufficiency content:
All of the above concepts, focused
on the “how” and “why” of a process
rather than the “what [is the answer]”
Evaluate sufficiency of 2 statements
Math Overview
Data sufficiency example:
“What is the value of x?
2
1) x = 9
A.
B.
C.
D.
E.
2) x is negative”
Statement 1 alone is sufficient; Statement 2 alone is not
Statement 2 alone is sufficient; Statement 1 alone is not
Both statements 1 and 2 together are sufficient; neither
statement alone is sufficient to answer the question
Each statement alone is sufficient to answer the question
Statements 1 and 2 together are not sufficient
Math Strategies
The GMAT contains relatively few
“one-step” problems. Nearly every
question will require more than one
calculation or test multiple concepts.
Remember, the easiest, most obvious
answers are often set up as traps.
Math Strategies
There are two good ways to tackle a
question you don’t know how to solve:
If the answers are algebraic, plug in
a number to simplify the question
If the answers are numbers, plug
each value into the question itself.
Math Strategies
“Jeremy can run 5 miles in 50
t minutes.
minutes.
If he can run x miles in 20 minutes, which
of the following is equal to the value of x?”
A. .5
t / 100
50
/ 100 = .5
D. .2
10 / t50 = .2
B. 5
t / 10
50
/ 10 = 5
E. 2
100 / t50 = 2
C. 50
t
= 50
Unless
Simplify
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Math Strategies
“Mr. Hooper’s Ice Cream Shop sells only
vanilla and chocolate. Today the ratio of
vanilla to chocolate cones sold was 2 to 3,
but if 5 more vanilla cones had been sold
the ratio would have been 3 to 4. How
many vanilla cones did he sell today?”
A. 20
B. 25
C. 30
D. 35
E. 40
Math Strategies
“… the ratio of vanilla to chocolate cones
sold was 2 to 3. If 5 more vanilla cones had
been sold the ratio would have been 3 to 4.
How many vanilla cones did he sell today?”
C. 20
30 / xB.= 225
/=3,35
= does
45
chocolate
A.
(30+5)/45
(20+5)/30
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Specific Content Review
Order of Operations
Perform arithmetic in this order:
1. Powers and square-roots
2. Multiplication and division
3. Addition and subtraction
But, anything in parentheses should
be solved first, from the inside out.
Order of Operations
Solve:
2 3
16 + 32 − 5
A. -20
D. 200
B. 5
E. 400
C. 128
2
Powers, Exponents, Roots
Exponents follow a few basic rules:
3
2
3+2
4 ∗ 4 = 4
4
6
2
5
=4
4 ∗ 4 ∗ 4 ∗ (4 ∗ 4)
4−2
2
6 =6
=6
6∗6∗6∗6
= (6 ∗ 6)
(6 ∗ 6)
Powers, Exponents, Roots
Exponents follow a few basic rules:
2
2
5 ∗ 6 = 5 ∗ 6
2
5 ∗ 5 ∗ 6 ∗ 6 = 5 ∗ 6 ∗ (5 ∗ 6)
3
5
3
3+2
3
2
2 ∗ 3 = 2 ∗ 3
= 2∗3 ∗3
2∗2∗2 ∗ 3∗3∗3∗3∗3 =
2∗3 ∗ 2∗3 ∗ 2∗3 ∗3∗3
Powers, Exponents, Roots
Exponents follow a few basic rules:
2 3
 7
2∗3
=7
=7
7∗7 ∗ 7∗7 ∗ 7∗7
−5
=1 2
1/3
3
2
8
6
5
=
8
Powers, Exponents, Roots
General facts about exponents:
A negative number to an even power
2
will be positive : −3 = −3 ∗ −3 = 9
A negative number to an odd power
3
will be negative: −2 = −2 ∗ −2 ∗ −2
Powers, Exponents, Roots
8
4
9 /
8
1 4
9
98 ∗ 1
2
4
−3
9 ∗3
4
−3
3 ∗3
3
6
1/2 6
/ 3
/ 36 ∗ 1/2
2 2
= 3
4−3
=3
−3
∗3
1
=3
Fractions, Ratios, Proportions
A fraction is a part divided by a whole:
7 𝑚𝑎𝑙𝑒𝑠

15 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠
or 7 divided by 15
A ratio is one part divided by another:
7 𝑚𝑎𝑙𝑒𝑠

8 𝑓𝑒𝑚𝑎𝑙𝑒𝑠
or a ratio of 7 : 8
Fractions, Ratios, Proportions
Fractions may be written in many
different equivalent ways. To find an
equivalent fraction, multiply or divide
the top and bottom of the original
fraction by the same number:
3

5
→
3
5
∗
2
2
→
3∗2
5∗2
→
6
10
Fractions, Ratios, Proportions
A proportion is a collective term for
a set of equivalent fractions or ratios:
3

5
1

2
=
6
10
=
2
4
=
=
15
25
5
10
=
=
30
50
6
12
=
=
60
100
10
20
= 𝑒𝑡𝑐
= 𝑒𝑡𝑐
Fractions, Ratios, Proportions
You will often need to be able to “solve
a proportion” on GMAT problems, as
in the prior ice cream shop example:
“If the ratio of vanilla to chocolate
cones sold is 2 to 3 and 30 vanilla
cones were sold today, how many
chocolate cones were sold today?”
Fractions, Ratios, Proportions
“If the ratio of vanilla to chocolate is
2 to 3 and 30 vanilla cones were sold,
how many chocolate cones were sold?”
Solve this step by setting up a set of
two equivalent ratios, a proportion:
2 30
=
3
𝑥
Fractions, Ratios, Proportions
You could solve this proportion using
algebra, or you can just think of what
number we multiplied the top and
bottom of the original fraction by:
2? 30
2 2 15
∗∗ =
3? 𝟒𝟓
𝑥
3 3 15
Operations using Fractions
Simplifying fractions:
Simplifying means to divide the top
and bottom by the same number;
this process may be repeated:
220

200
→
1/2
220/10
1/2
200/10
=
22
20
→
22/2
20/2
=
11
10
Operations using Fractions
Reciprocals of fractions:
If asked to divide 1/x where x is any
fraction, the answer is to “flip” x:
1

3 5
=
5
3
Operations using Fractions
Reciprocal relationships:
If two fractions are equal, you can
flip both and they will still be equal:
220

200
=
11
10
→
200
220
=
10
11
Operations using Fractions
Addition or subtraction:
Make each fraction have the same
bottom number using a proportion,
then add/subtract the top numbers:
33 ∗ 4
2
 +
55 ∗ 4
+
2∗5
4∗5
→
12
20
+
10
20
→
22
20
→
11
10
Operations using Fractions
Multiplication or division:
For multiplication, multiply the 2 top
and 2 bottom numbers; for division,
flip the 2nd fraction, then multiply:
2 44
22 ∗ 45
28 ∗ 5
→ ∗ →
 /∗ →
→
15
3 55
33 ∗ 54
3∗4
→
10
12
→
5
6
Operations using Fractions
Combining numbers and fractions:
Any number x may be written as x/1,
or as any fraction that simplifies to it:
5
6
3
1
5
6
3 ∗ + 2 → ∗ +
12
6
→
15
6
+
12
6
=
27
6
Operations using Fractions
If
1
𝑥
=
3
2
solve:
1
𝑥+2
2
A. 9/64
D. 64/9
B. 16/9
E. 9/16
C. 4/9
Percent & Percent Change
A percentage is a fraction over 100:
57% =
57
100
‘x percent of y’ is x written as a fraction
over 100 multiplied by the value of Y:
35% 𝑜𝑓 400 𝑖𝑠 … ? →
35
100
∗ 400 = 120
Percent & Percent Change
Use proportions to solve percentages:
Of the 400 trucks for sale on a used
car lot, 120 have air-conditioning;
what percent of trucks have a/c?
120

𝑖𝑠
400
𝑤ℎ𝑎𝑡 %? →
120
400
𝑥
∗=100
100
= 30%
𝑥
Percent & Percent Change
An “x percent change” is calculated as
the proportion of the amount of the
change over the original amount:
“If a home was purchased for $200k
and sold for $230k, by what percent
did the home appreciate in value?”
Percent & Percent Change
“If a home was purchased for $200k
and sold for $230k, by what percent
did the home appreciate in value?”
𝑥30
𝑐ℎ𝑎𝑛𝑔𝑒
==
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 100
200
𝑥
∗=100
100
=
𝑥 𝑥
𝑥
15%
100 100
Percent & Percent Change
The GMAT contains many problems
that make use of multiple percentages.
Although it is possible to solve these
using proportions and/or algebra, it is
better to plug in a starting value of 100
and calculate other values as you go.
Percent & Percent Change
“60 percent of Loyola seniors are female.
If 40 percent of females and 30 percent of
males have studied abroad in this year’s
senior class, what is the total percent of
Loyola seniors that have studied abroad?”
A. 24 B. 30 C. 36 D. 42 E. 70
Percent & Percent Change
“60 percent of seniors are female… 40
percent of females and 30 percent of males
have studied abroad… what is the total
percent that have studied abroad?”
A. 24
B. 30
C. 36
D. 42
E. 70
So,percent
You
Instead,
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imagine
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24females
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females
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If so,proportions,
and
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40
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males
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and
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40
shouldn’t.
males
= 36%.
= 12
Probability & Permutations
Probability is a ratio or percentage
equal to the # of desired outcomes
over the # of all possible outcomes:
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓𝑑𝑟𝑎𝑤𝑖𝑛𝑔 𝑎𝑛 𝐴𝑐𝑒 =
4 𝑎𝑐𝑒𝑠
52 𝑐𝑎𝑟𝑑𝑠
=
1
13
= ~7.7%
Probability & Permutations
There are 3 probability rules you need:
1. a AND b together = Pr a ∗ Pr b
2. either a OR b = Pr a + Pr(b)

If a and b can occur together, the
rule is: Pr a + Pr b − Pr(a and b)
3. a does NOT occur = 1 − Pr a
Probability & Permutations
Like all GMAT problems, probability
concepts are often tested 2 at a time:
“set 1 = {a, b, c, d, e} set 2 = {f, g, h, i, j}
If you choose 1 letter at random from
each set above, what is the probability
that you do get at least one vowel?”
Probability & Permutations
“set 1 = {a, b, c, d, e} set 2 = {f, g, h, i, j}
What is the probability that you get at
least one vowel choosing 1 from each?”
PrPr
Pr𝑣𝑜𝑤𝑒𝑙
𝑣𝑜𝑤𝑒𝑙
𝑣𝑜𝑤𝑒𝑙
𝑖𝑛𝑖𝑛
𝑖𝑛𝑠𝑒𝑡
𝑠𝑒𝑡
𝑠𝑒𝑡11type
1𝑂𝑅
𝑂𝑅
𝑂𝑅𝑣𝑜𝑤𝑒𝑙
𝑣𝑜𝑤𝑒𝑙
𝑣𝑜𝑤𝑒𝑙
𝑖𝑛𝑖𝑛
𝑖𝑛𝑠𝑒𝑡
𝑠𝑒𝑡
𝑠𝑒𝑡You
222 can
This
is
a common
of
problem.
=2the
Pr
+ Pr 5𝑣𝑜𝑤𝑒𝑙
use
“a
b”
subtracting
22 2𝑖𝑛
1 1formula,
2 1𝑣𝑜𝑤𝑒𝑙
1 OR
10
2 𝑖𝑛 213 “a
=−
+
−
∗
= Pr
+
−
→
+
−
=
𝑖𝑛
𝐴𝑁𝐷
∗ Pr(𝑣𝑜𝑤𝑒𝑙
𝑣𝑜𝑤𝑒𝑙
𝑖𝑛
𝑖𝑛together.
2)
2)25
AND
because
can
5Pr(𝑣𝑜𝑤𝑒𝑙
5 25
5 1both
5b”5𝑣𝑜𝑤𝑒𝑙
5 25
25
25occur
25
Probability & Permutations
“set 1 = {a, b, c, d, e} set 2 = {f, g, h, i, j}
What is the probability that you get at
least one vowel choosing 1 from each?”
PrPr𝑁𝑂𝑇
𝑁𝑂𝑇
𝑐𝑜𝑛𝑠𝑜𝑛𝑎𝑛𝑡
𝑐𝑜𝑛𝑠𝑜𝑛𝑎𝑛𝑡
𝑖𝑛
1 the
𝐴𝑁𝐷
1 𝐴𝑁𝐷
𝑖𝑛𝑖𝑛
22
You
can
also
solve this𝑖𝑛as
probability
that
your
choice
NOT
consonants,
=1
−
Pr(𝑐𝑜𝑛𝑠𝑜𝑛𝑎𝑛𝑡
1 ∗𝑖𝑛two
Pr(𝑐𝑜𝑛𝑠.
1 𝐴𝑁𝐷
𝑖𝑛
𝑖𝑛 2)
2)
3 Pr
4 𝑐𝑜𝑛𝑠.
25is𝑖𝑛12
12
13
1 −−
=
1
−
∗
→
=
or 1 – Pr(consonant
in
1 AND set 2).
5 5 25 25
25set 25
Probability & Permutations
A permutation (or combination) is the
number of ways to order (or select) a
number of choices from a given set.
𝑊𝑎𝑦𝑠 𝑡𝑜 𝑐ℎ𝑜𝑜𝑠𝑒 3 𝑖𝑡𝑒𝑚𝑠 𝑜𝑢𝑡 𝑜𝑓 6
6∗5∗4
=
= 20
3∗2∗1
†: a combination
†
Probability & Permutations
For an ordered set (“arrangement”),
multiply together the number of
options still remaining at each choice.
𝐻𝑜𝑤 𝑚𝑎𝑛𝑦 𝑤𝑎𝑦𝑠 𝑐𝑎𝑛 𝑦𝑜𝑢 𝑠𝑒𝑎𝑡
4 𝑝𝑒𝑜𝑝𝑙𝑒 𝑖𝑛 5 𝑐ℎ𝑎𝑖𝑟𝑠?
= 5 𝑐ℎ𝑎𝑖𝑟𝑠 ∗ 4 ∗ 3 ∗ 2 = 120
Probability & Permutations
For an unordered group (“selection”),
divide the full ordered count by the
number of ways to order the choices.
𝐻𝑜𝑤 𝑚𝑎𝑛𝑦 𝑤𝑎𝑦𝑠 𝑐𝑎𝑛 𝑦𝑜𝑢 𝑐ℎ𝑜𝑜𝑠𝑒
3 𝑜𝑓𝑓𝑖𝑐𝑒𝑟𝑠 𝑓𝑟𝑜𝑚 7 𝑛𝑜𝑚𝑖𝑛𝑒𝑒𝑠?
𝑜𝑟𝑑𝑒𝑟𝑒𝑑 = 210;
7
210
𝑛𝑜𝑚𝑖𝑛𝑒𝑒𝑠
𝑤𝑎𝑦𝑠 𝑡𝑜∗𝑜𝑟𝑑𝑒𝑟
6 ∗ 5 = 6210
𝑜𝑣𝑒𝑟𝑎𝑙𝑙
3 𝑐ℎ𝑜𝑖𝑐𝑒𝑠
==
𝑜𝑟𝑑𝑒𝑟𝑒𝑑
210
3 ∗62=∗ 35
𝑤𝑎𝑦𝑠
1 =𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑠
6 𝑡𝑜 𝑜𝑟𝑑𝑒𝑟
Probability & Permutations
“To fill a number of vacant positions,
an IT firm needs to hire 2 database
administrators from 6 applicants,
and 3 developers from 5 applicants.
How many selections could be made?”
A. 25
B. 60
C. 150 D. 180 E. 1800
Averages & Variation
“Mean, median, and mode”:
Mean (or average) is the sum of all
values divided by the count of values.
Median is the “middle” number in a
set of values when put in rank-order.
Mode is the most frequent value.
Averages & Variation
{3, 4, 6, 7, 7, 9}
Mean =
3+4+6+7+7+9
6
=
36
6
=6
Median = ½-way between 6 and 7 = 6.5
Mode = 7
Averages & Variation
The mean (or average) has 3 parts:
𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑣𝑎𝑙𝑢𝑒𝑠
𝑚𝑒𝑎𝑛 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠
GMAT questions commonly test the
ability to apply this formula in an
unexpected “direction” or context
Averages & Variation
“A company has two sales teams, A and B,
with 4 and 6 salespeople respectively. If the
average number of monthly sales generated
by salespeople in team A is 20 sales and the
average in team B is 30 sales, what is the
overall average number of sales generated?”
Averages & Variation
“If average sales in team A (4 people) is 20
and average sales in team B (6 people) is
30, what is the overall average # of sales?”
80
+25𝑜𝑓
180
260
𝑠𝑢𝑚
𝑜𝑓
𝑠𝑢𝑚
𝐴wrong,
𝑎𝑙𝑙
+ 𝑜𝑓
𝑠𝑢𝑚
𝑣𝑎𝑙𝑢𝑒𝑠
𝐴but
(20
∗is
4)
(30
∗𝑜𝑓
6)𝐵
The “obvious” answer𝑠𝑢𝑚
of
𝑎𝑣𝑒𝑟𝑎𝑔𝑒
𝑜𝑣𝑒𝑟𝑎𝑙𝑙
𝑎𝑣𝑒𝑟𝑎𝑔𝑒
20
== = 4 = =
𝑠𝑢𝑚 𝑜𝑓=𝐴26
𝑜𝑣𝑒𝑟𝑎𝑙𝑙
𝑎𝑣𝑒𝑟𝑎𝑔𝑒
𝑎𝑣𝑒𝑟𝑎𝑔𝑒
𝑜𝑓∗𝐴𝑛𝑢𝑚𝑏𝑒𝑟
(20)
maybe it is not obvious
why
so.
10
𝑓this
4𝑓𝑛𝑢𝑚𝑏𝑒𝑟
𝑓𝑟𝑜𝑚
𝑛𝑢𝑚𝑏𝑒𝑟
+
𝑜𝑓is6
𝑖𝑛
𝑣𝑎𝑙𝑢𝑒𝑠
𝑓𝑟𝑜𝑚
𝐴 (4)𝐵
𝑓𝐴 10
𝑓10
So
overall
sales
is 26
Rearranging
the
formula,
we
can
find
that
To the
solve
find
number
the
forthis
overall
sum
the
ofaverage
sales
overall
of
sum
values
figures
average,
of
from
values,
being
each
take
you
averaged
team,
this
will
The
average
of
A,
20,
isnumber
equal
toof
the
sum
of
Following
logic,
we
can
fill
in
the
total
which
different
from
the
obvious
answer.
formula
is
need
you
4 sum
from
have
toisknow
and
to
team
start
the
Ateams
the
and
sum
filling
average
6the
from
from
in
what
of
each
team
you
team..
team.
know.
or 10.
A
(unknown)
divided
by
the
4each
salespeople.
sum
from
both
A
and
B,
then
solve.
the
of
Ause
must
be
average
*B,count.
Averages & Variation
“The average of a set of 9 numbers is 8.
Two of the numbers are 11 and 12. What
is the average of the remaining values?”
A. 4.5 B. 5
C. 5.4 D. 6
E. 7
Averages & Variation
Range and Standard Deviation:
The range of a set of values is the
highest value – the lowest value.
The standard deviation is a number
that represents an average “distance
from the mean” in the set of values.
Averages & Variation
{3, 4, 6, 7, 7, 9}
Range = 9 – 3 = 6
St. Dev. = approx. 2
Mean
↓
Data →
0
1
2
3
4
5
Dist. = 2
Dist. = 3
6
7
8
Dist.=1
Dist. = 3
9
Averages & Variation
Standard Deviation concepts:
Two sets of data with different
means do not necessarily have
different standard deviations.
Distance from the mean, not other
data points, determines the std. dev.
Averages & Variation
Set S has a mean of 10 and a std. dev. of 3. We are
going to add two numbers to Set S. Which pair of
numbers would decrease the std. dev. the most?
A. {2, 10}
B. {10, 18}
C. {7, 13}
D. {9, 11}
E. {16, 16}