MATH 2160 4th Exam Review

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MATH 2160 4th Exam Review

• Statistics and Probability

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Problem Solving Polyas 4 Steps

• Understand the problem
• What does this mean?
• How do you understand?
• Devise a plan
• What goes into this step?
• Why is it important?
• Carry out the plan
• What happens here?
• What belongs in this step?
• Look back
• What does this step imply?
• How do you show you did this?

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Problem Solving

• Polyas 4 Steps
• Understand the problem
• Devise a plan
• Carry out the problem
• Look back
• Which step is most important?
• Why is the order important?
• How has learning problem solving skills helped
  you in this or another course?

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Problem Solving

• Strategies for Problem Solving
• Make a chart or table
• Draw a picture or diagram
• Guess, test, and revise
• Form an algebraic model
• Look for a pattern
• Try a simpler version of the problem
• Work backward
• Restate the problem a different way
• Eliminate impossible situations
• Use reasoning

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Statistics

• Mean
• Most widely used measure of central tendency
• Arithmetic mean or average
• Sum the terms and divide by the number of terms
  to get the mean
• Good for weights, test scores, and prices
• Effected by extreme values
• Gives equal weight to the value of each
  measurement
• or

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Statistics

• Median
• Put the data in order first
• Odd number of data points choose the middle term
• Even number of data points take the average of
  the middle two terms
• Used when extraordinarily high or low numbers are
  included in the data set instead of mean
• Can be considered to be a positional average

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Statistics

• Mode
• The mode occurs most often. If every measurement
  occurs with equal frequency, then there is no
  mode. If the two most common measurements occur
  with the same frequency, the set of data is
  bimodal. It may be the case that there are three
  or more modes.
• Used when the most common measurement is desired
• Finding the best tasting pizza in town

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Statistics

• Range
• The difference of the highest and lowest terms
• Highest lowest range
• Radically effected by a single extreme value
• Most widely used measure of dispersion

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Statistics

• Measures of Central Tendency
• Mean
• Median
• Mode
• Measures of dispersion
• Range

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Statistics

• Experimental Error
• Absolute value of the difference between an
  experimental or estimated value and a theoretical
  or known value divided by the theoretical or
  known value

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Statistics

• Types of Data
• Interval/ratio temperatures, prices, test
  scores, etc.
• Ordinal low, medium, high
• Nominal red, blue, green
• Discrete people, keys, desks, etc.
• Ordinal
• Nominal
• Interval/ratio
• Continuous - temperatures, prices, test scores,
  etc.
• Interval/ratio

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Statistics

• Line Plot
• Useful for organizing data during data collection
• Categories must be distinct and cannot overlap
• Not beneficial to use with large data sets

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Statistics

• Bar graph
• Another way of representing data from a frequency
  line plot
• More convenient when frequencies are large

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Statistics

• Line graph
• Sometimes does a better job of showing
  fluctuation in data and emphasizing changes
• Uses and reports same information as bar graph

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Examples

• Test scores
• 89, 73, 71, 46, 83, 67, 83, 74, 76, 79, 81, 84,
  105, 84, 85, 99, 48, 74, 60, 83, 75, 75, 82, 55,
  76
• Mean Sum of scores/Number of scores
• 1906/25
• 76.25

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Examples

• Test scores
• 46, 48, 55, 60, 67, 71, 73, 74, 74, 75, 75, 76,
  76, 79, 81, 82, 83, 83, 83, 84, 84, 85, 89, 99,
  105
• Median 76
• Mode 83
• Range 105 46 59

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Examples

• Keys in Pockets
• 1, 2, 2, 3, 5, 6, 8, 5, 2, 2, 4, 1, 1, 3, 5
• Line Plot

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Examples

• Keys in Pockets
• 1, 2, 2, 3, 5, 6, 8, 5, 2, 2, 4, 1, 1, 3, 5
• Bar Graph

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Examples

• Keys in Pockets
• 1, 2, 2, 3, 5, 6, 8, 5, 2, 2, 4, 1, 1, 3, 5
• Line Graph

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Probability

• Sample space ALL possible outcomes
• Experiment an observable situation
• Outcome result of an experiment
• Event subset of the sample space
• Probability chance of something happening
• Cardinality number of elements in a set

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Probability

• 0 ? P(E) ? 1
• P(?) 0
• P(E) 0 means the event can NEVER happen
• P(E) 1 means the event will ALWAYS happen

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Probability

• P(E) is the compliment of an event
• P(E) P(E) 1
• P(E) 1 P(E)

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Probability

• Experiment Examples
• Sample Spaces
• One coin tossed S H, T
• Two coins tossed S HH, HT, TH, TT
• One die rolled S 1, 2, 3, 4, 5, 6
• One coin tossed and one die rolled S
  H1, H2, H3, H4, H5, H6, T1, T2, T3, T4,
  T5, T6

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Probability

• Experiment Examples
• Cardinality of Sample Spaces
• One coin tossed S H, T
• n(S) 21 2
• Two coins tossed S HH, HT, TH, TT
• n(S) 22 4
• One die rolled S 1, 2, 3, 4, 5, 6
• n(S) 61 6
• One coin tossed and one die rolled S
  H1, H2, H3, H4, H5, H6, T1, T2, T3, T4,
  T5, T6
• n(S) 21 x 61 12

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Probability

• Probability of Events
• What is the probability of choosing a prime
  number from the set of digits?
• S 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• E 2, 3, 5, 7
• n(S) 10 and n(E) 4
• P(E) n(E)/n(S) 4/10 2/5 0.4
• The probability of choosing a prime number from
  the set of digits is 0.4

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Probability

• Probability of Events
• What is the probability of NOT choosing a prime
  number from the set of digits?
• S 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• E 2, 3, 5, 7
• n(S) 10 and n(E) 4
• P(E) n(E)/n(S) 4/10 2/5 0.4
• P(E) 1 P(E) 1 0.4 0.6
• The probability of NOT choosing a prime number
  from the set of digits is 0.6

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• I think you all will probability pass this test
  without any trouble!! ?
• Just like puttin money in the bank!!! ?

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Test Taking Tips

• Get a good nights rest before the exam
• Prepare materials for exam in advance (scratch
  paper, pencil, and calculator)
• Read questions carefully and ask if you have a
  question DURING the exam
• Remember If you are prepared, you need not fear