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34 Cards in this Set
- Front
- Back
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Distributions are used for:
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1. Description of the data
2. Analysis of the data |
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What are the two general types of distributions?
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Observed
and Standard |
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Standard distributions are also known as:
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Theoretical
or Probability Distributions |
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What are the steps in preparing an Observed Distribution?
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1. Collection of numbers (measurements of a variable).
2. Sort the numbers (e.g. ordered array). 3. Classify the data - group in bands 4. Prepare frequency table 5. Prepare frequency histogram Stop here if only for descriptive purpose; otherwise, 6. Prepare a probability histogram (change the vertical axis units to probabilities). |
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Data points are sometimes referred to as:
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Observations
or Readings |
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Define an Ogive
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a cumulative frequency table put into the form of a graph
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The probabilities of mutually exclusive vents can be:
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added together.
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Define conditional probability
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the probability of an event under the condition that another event has occurred or will occur.
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What is the addition law for mutually exclusive events
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P(A or B or C or ...) = P(A) + P(B) = P(C) + ...
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Define conditional probability
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the probability of an event under the condition that another event has occurred or will occur.
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What is the multiplication law of probability for independent events?
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P(A and B and C and ..) =
P(A) x P(B) x P(C) x ... |
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Define combination
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the number of different ways in which r objects can be chosen from a total of n objects.
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Describe standard distribution
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one that has been defined mathematically from a theoretical situation.
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How are probabilities measured for standard distributions?
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A priori method
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Describe normal distribution
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a standard distribution which was derived from the theoretical situation of a variable being generated by a process which should give the variable a constant variable.
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What does the use of observed distribution imply versus use of standard distribution?
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Use of Observed Distribution implies that data has been collected, probabilities calculated and histograms formed.
Use of the Standard Distribution implies that the situation in which the data being generated resembles closely a theoretical situation for which a distribution has been constructed mathematically. |
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Describe binomial distribution
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Distribution which:
a. is discrete b. has a stepped shape c. can vary from right-skewed to symmetrical to left-skewed d. outcomes are mutually exclusive |
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Some situations in which binomial is used:
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a. inspection schemes (quality)
b. opinion polls c. selling |
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How are binomial probabilities calculated?
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a. mathematically used formula which is provided
b. by using binomial tables (also provided) |
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Define distribution parameters
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fix the context within which the variables vary
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How to decide if data fits binomial
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physical check to see if the proportion meets the expected.
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What is the most known and used standard distribution?
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The normal distribution
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Describe normal distribution
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a. bell shaped
b. symmetrical |
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How is probability measured for discrete and continuous distributions?
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for discrete - by height of column
for continuous - by the area under the graph |
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What are the Standard Deviation attributes for Normal Distributions?
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68% of readings lie within +/- 1 standard deviation
95% of readings lie within +/- 2 standard deviations 99.7% of readings lie within +/- 3 standard deviations |
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Actual situations in which the normal distributions apply.
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a. IQs of children
b. heights of people of the same sex c. dimensions of mechanically produced components d. weights of machine-produced items e. arithmetic means of large samples |
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One of most important uses of the normal distribution
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In Sampling
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What are parameters for normal distribution?
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Arithmetic mean and standard deviation
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What are the parameters for binomial distribution?
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Sample size and population proportion of type 1.
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How to decide if data fits normal distribution
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Calculate the arithmetic mean and standard deviation of observations. Then compare the observed to theoretical % to see if these reasonably match. This is judgement call.
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When is binomial symmetrical?
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When p is not close to 0, or when n is large.
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When can the normal be used to approximate the binomial?
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When np and n(1-p) both exceed 5.
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To use normal distribution, what info must be known?
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Arithmetic mean and standard deviation
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What is formula for calculating mean and standard deviation for binomial?
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Mean = np and Standard Deviation = the square root of np(1 - p)
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