Variable/Random Variable (X)
represents a quantitative (numerical) value that is measured/observed in an experiment
Nominal and Ordinal are what type of variable?
Discrete; can only take on whole numbers
Interval and Ratio are what type of variable?
Continuous; can take on any value
Discrete Random Variable
finite, infinitely countable; can only take on particular values; arise from COUNTING
Continuous Random Variable
infinite number of possible values in an interval of numbers; arise from MEASURING
Probability Distribution
assignment of probabilities to all the possible values of a random variable; lists all the possible values of x and their corresponding probabilities
Discrete Probability Distribution
-probability of x between 0 and 1 or 0% and 100%
-probability of all x values adds up to 1 or 100%
What probability of a variable is considered unusual for a discrete variable?
value of 0.05 or 5.00%
P(X ≥ 0.05) means:
x is an unusually high value
P(X ≤ 0.05) means:
x is an unusually low value
Does the mean of a random variable need to be a possible value of x?
No
The mean can also be thought of as the:
expected value; the one you would find on average
Does the mean/expected value need to be a whole number?
No
In discrete probability distribution, how many outcomes/groups can a person/case belong to?
Only one
Continuous Random Variable (X)
variable with infinite number of random values in an interval of numbers
Empirical Rule (68-95-99.7)
In a bell-shaped distribution,
-68% data within 1 standard deviation of the mean
-95% data within 2 standard deviation of the mean
-99.7% data within 3 standard deviation of the mean
Normal/Gaussian Distribution
special type of distribution for CONTINUOUS random variable
What shape is the graph of normal distribution?
symmetrical bell-shaped curve
How many modes does normal distribution have?
One; unimodal
What is the centre of a normal distribution graph?
Mean
What is the total area under a normal distribution curve?
1 or 100%
How is the spread of normal distribution determined?
by the standard deviation; larger standard deviation, more spread out curve
What rule does normal distribution follow?
Empirical rule
Standard Normal Distribution
normal distribution with mean µ = 0 and standard deviation σ= 1
