GRE Review

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GRE Review

• Data Analysis

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Some basics

• The mean The average of the values. Just add up
  the values and divide by the number of values.
• If I said the average of x, y and 5 is 11, you
  would write this as
• The median the middle number when the numbers
  are written in order. If there are 2 middle
  numbers (i.e. an even number of data values),
  just average those two middle numbers to get the
  median.
• The mode the number that occurs most often

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Measures of dispersion

• Range difference between the high and low
  values (not extremely useful)
• Standard Deviation -
• Sample

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Standard Deviationby hand

• Below are the times (in min) it took for the
  Dominos to deliver a pizza to our house
  22,30,27,39. Find the standard deviation
  (sample).
• Step 1. Find . In our problem

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• Step 2. Create the table shown below

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• Step 3. Use the formula

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Classical Probability

• To find the probability of an event
• Assumption All events are equally likely. (e.g.
  when a die is rolled)

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Example

• Find the probability of rolling a 3 on 1 roll of
  one die.

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Example

• Find the probability of selecting a king with one
  draw from a deck of cards.

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Probability Rules

• The probability will always be between 0 and 1,
  inclusive.
• If the probability is certain to occur, the
  probability is 1
• If the probability cannot occur, then the
  probability is 0.
• The sum of the probabilities for a sample space
  is 1.

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Complementary Events

• the probability of an event A. not occurring,
  denoted as . Mathematically

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Example

• If the probability of dying from a certain
  procedure is 1/3, find the probability of not
  dying.

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• To determine the probability of a compound event
  when we are looking for event A occurring or
  event B occurring, we should find the total
  without counting it twice.

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Example 1

• Find the probability of rolling a 2 or a 3 with
  one roll of 1 die.

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Addition Rule Formula 1

• Formula 1

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Example

• A single card is drawn from a deck of cards.
  Find the probability of selecting a 6 or a club.

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Addition Rule Formula 2

• Formula 2

If events A and B cannot occur together they are
called mutually exclusive (that is,
)
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Example
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Multiplication Rule 1

• When A and B are independent

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Example

• Flip a coin 2 times. What is the probability
  that we get 2 heads?

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Multiplication Principle

• Take the number of ways you can do event 1 and
  multiply it by the number of ways you can do
  event 2, etc

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Example
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Example

• How many different license plates are possible if
  a state uses the format of 3 letters followed by
  3 numbers.
• 17,576,000

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Example Permutations

• How many ways can you select a president and a
  vice president from a group of 20 people?
• Not 20!
• We can use a permutation

n total of objects
r of objects used
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Example (cont)

• In our problem n 20 and r 2

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Combinations

• How many ways can you select a 4 person committee
  from a group of 20 people.
• How does this problem differ from the previous?
• The order of the how the committee members does
  not matter. That is a committee of Lindsey,
  Becca, Chase, and Justin would be the same as a
  committee of Chase, Lindsey, Justin Becca.

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Combinations (cont)

• So we need to divide out all of the times we are
  counting the same committee. This yields the
  following formula

In our problem, n 20 and r 4.
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Perm. vs Comb. vs Mult. Prin.

• When the ordering matters, select permutations
  when the order does not matter, select
  combinations.
• When items are allowed to repeat, you cannot use
  either one. You must use the multiplication
  principle.

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Reading and interpreting Graphs and Charts

• Be sure to read all of the labels
• Be sure to read the questions to ensure that you
  are using the correct graph.