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ST370 Prob & Statistics for Engineers NC State, complete
Definitions
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Population The entire collection of subjects we wish to target
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Sample A subset of the population
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Univariate 1 variable
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Bivariate 2 variables from the same subject
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Multivariate 2 or more variables from the same subject
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Qualitative Data Categorical, descriptive (yes/no, blue, etc)
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Quanitative Data Numeric (include discrete and continous)
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Discrete Data Primarily count data (the number of...)
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Continuous Data Data from measurements (can take on any value w/in some interval)n
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Ways to Obtain a Sample
Stratified Sample |
helps avoid biased data (If there are 2X white people than Hispanics, then the sample should have 2X white people than Hispanics) |
Convenience Sampling |
Stay away from this, (Choosing to only sample from one assembly line on the shop floor) |
Simple Random Sampling |
(A name is drawn out of a hat) |
Ways to Obtain Data
Experiment |
allows us to draw cause and effect b/c of the ways its designed (the best) |
Survey |
A questionnaire or observation |
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The 2 Branches of Statistics
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Descriptive Statistics use of graphs, numeric computations to summarize the data
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Inferential Statistics Make and inference using sample statistics back to the population
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____ Predicts _____
Sample Mean (x ̅) |
Population mean (μ) |
Sample Median (x ̃) |
Population Median(μ ̃) |
Sample Relative Frequency (p ̂) |
Population Proportion (p) |
Sample Standard Deviation (s) |
Population Standard Deviation (σ) |
Sample Variance (s2) |
Population Variance (σ2) |
Things to know how to calculate:
Trimmed Mean |
trim a certain percentage of values from the ends of the data set, and then average whats left |
Standard deviation (s) |
The size of a typical deviation (calculator function) |
Variance (s2) |
How data points vary from the mean |
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Symbols and Their Meanings
n |
sample size |
N |
population size |
Characteristics of a Graph
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Center tells us what a typical value in the data set should be (If data is fairly symetric use mean, otherwise, use median)
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Spread The range of data
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Skew If the bell curve is shifted left (negative skew) or right (positive skew)
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More on Box Plots
Box Plots |
They show us outliers visually, and are great for comparing multiple data sets |
Quartiles |
Values that divide the sorted data set into 4 equal parts. |
Q1 |
The smallest 25% of data |
Q2 |
The median |
Q3 |
The 75% mark |
Q4 |
The max value |
percentiles |
If a value is in the first quartile, then 75% of the values are grater than that, so your in the 75th percentile |
Graph Types
Box Plots |
Show us outliers visually and great for comparing multiple data sets |
Dot Plot |
Dots located above their value on the X-axis |
Stem and Leaf |
The stem of the number includes all but the last digit (so 38|3 would be 38.3) |
Histogram |
Like box graphs but there's no spaces between columns, can be used with discrete and continuous data |
Histogram Shapes: |
Symmetric, Right(positive) skew, Left (negative) skew, Bi-modal (2 peaks), and Multi-modal (many peaks) |
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