Stats 1124: CH 2
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What is the mean?
- The measures of the average!
- Symbol: x(with line on top)
What is the Median?
Median(m): the value that has the middle position when n data points are put in order
Compare Mean and Median in two ways
1. If graph is mound and symmetric, mean and median are the same.
2. If graph is skewed, mean moves away from the median toward the longer tail
Why is median a resistant measure?
Because it is NOT affected by an extreme observation(change).
What are thw two measures of variablility?
- 1. Range
- 2. Standard Deviation
What does the range give us?
Range(R) = MAX - MIN , it gives us the spread of the entire data
Why can the range be misleading? (2)
What is standard Deviation?
(s): It uses all the data points and describes the variation around the mean.
It is a concept not a calculation!
What is degrees of freedon? (df)
Idea: The number of observations that are free to vary after the sample mean has been calculated
What are the four properties of standard deviation?
What is the five-number summary?
What is interquartile range (IQR)?
(Q3 - Q1): It gives us the spread of the middle 50% of the data
What two values gives us the range?
(Q1 - 1.5 x IQR) and (Q3 + 1.5 x IQR)
What are suspected outliers?
Any values that fall outside this range (Q1 - 1.5 x IQR) and (Q3 + 1.5 x IQR)
How are boxplots best used?
They are best used by a side-by-side comparison
Why are Histograms only in 5 to 10 intervals?
Bceause too many points(50) or too little (2) will cause the shape to look unappealing.
- 50 points = not summarized enough
- 2 points = too summarized
What are three things about a Histogram thats different?
- 1. large dataset
- 2. left inclusion
- 3. no overlap
What are 4 things to look for when looking at the graph?
- 1. Centre:(Midpoint)
- 2. Spread:(Range)
- 3. Outlier: (unusual points)
- 4. Shape:( Symmetrical, skewed right and left)
How can mean by increased and decreased?
Mean can be increased by adding more data points and decreased by removing datapoints
How to check if something is resistant or not?
- Check if it affects the outliers.
- Mean is sensitive to the influence of extreme observations(Changes a lot when something is added or deleted), therefore, NOT RESISTANT.
If something is resistant to something then it DOESN'T change a lot, if it is NOT resistant to something then it CHANGES easily.
Is range a resistant outlier?
Range is NOT a resistant outlier.
Is Median resistant or not?
Median IS resistant
What would you like to do?
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