6. Quantitative Methods and Tools Flashcards
Type of data - example (1, 2, 3, 4)
Discrete Data (Attributes)
Type of data - example (1.25, 5.49, 3.12)
Continuous Data (Variables)
Nominal
Can only count items
Indicates characteristic by name, category, number, presence/absence
Ordinal
Order is important
Grouping into categories having an attribute
Fixed or defined scale but no true zero
Potential zero point
Interval
There is a true zero
Can add, subtract, multiply and divide values
Ratio
Range, standard deviation, and variation describe..
Dispersion
Distribution of sample averages will tend toward a normal distribution as the sample size (n) increases. Thus, the sampling distribution of the mean will follow a normal distribution with a certain mean and standard deviation.
Central Limit Theorem
- Shows the pattern of variability around the center.
- Organizes information for ease in calculating the statistics, such as the sample mean and the sample standard deviation.
- The number of classes should be at about the square root of the sample size
Frequency Distributions
A type of histogram, 1st digit, 2nd digit…
Stem-and-Leaf Plots
Use five key data points to graphically compare data produced from different sources (different machines, operators, etc)
Box-and-Whisker Plots
Probability Plots are used to…
Used to determine the type of distribution from which a set of data may have come
The _______ of any single observation, xi, is the mean of the population, μ , from which the observation has come. The notation is given as E(xi) = μ
Expected Value
- Making a hypothesis of what we expect to find
- Collecting data
- Analyzing the data
- Drawing a conclusion about the validity of the hypothesis
Analytical Studies
Type of distribution where:
Most of the data points are concentrated around the average (bell shaped curve)
Normal Distribution
Type of distribution where:
Equal probability of outcomes
Uniform Distribution
Type of distribution where:
Variables are distributed jointly
Bivariate Normal Distribution
Which type of distribution:
Analyzes reliability. Similar to Poisson, is used to determine the average time between failures or average time between a number of occurrences
Examples - time between events, time to
Exponential Distribution
Which type of distribution:
Skewed-right with most data in the left tail, and consisting of the distribution of the random variable whose natural logarithm follows the normal distribution
Examples - response time, time-to-failure data, and time-to-repair data
Lognormal Distribution
Which type of distribution:
• β is the shape parameter – defines the probability distribution function
• θ is the scale parameter – describes the magnitude of the x-axis
• Both are greater than zero
Weibull Distribution – analyzed reliability.
Similar to lognormal
Examples - time to fail, time to repair, and material strength