construction engineering 221 probability and statistics
TRANSCRIPT
Construction Engineering 221
Probability and statistics
Data description
• Random sample- every member of the population has an equal chance of being selected into the sample. Hard to do (unlisted phone #’s, no permanent address)
• Can use random number generator
• Non-random is OK if biases are known and reported
Data description
• Data from the sample represent an array (rows and columns) in raw form- how it might look on an Excel spreadsheet
• Can organize the data in various ways to simple the array and make it more “readable”– Classification- like letter grades, use class
intervals to combine similar scores
Data description
– Class boundaries separate one class from another
– Edges of boundaries are “class limits”, and represent the data where most information is “lost”
– Class size, interval, and boundary are arbitrary– Class mark is the midpoint of the class limits
Data description
• Class frequencies are the number of scores within each class
• The list of frequencies forms a distribution that typically assumes one of several standard forms (Normal, Chi Square, Poisson, Binomial)
• Cumulative distribution is a representation of number of scores below. When divided by total, the number represents a percentile rank
Data description
• Histogram is a common graphical representation of a frequency distribution
• Frequency polygon connects the midpoints of the histogram class limits and represents data distribution as a line
• Ogive- cumulative distributions- normal distribution will have an S-shaped ogive
Data description• Common engineering distributions
WeibullPoissonPower log normal
Binomial Chi square Log normal Normal