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13 Cards in this Set

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Range v Interquartile Range (IQR)
Range: Max-Min
IQR: Q3-Q1
Advantages of IQR and Range
1.Simple to compute
2. IQR not sensitive to outliers
Disadvantages of Range and IQR
1.Don't involve actual values of all data points
2.not commonly used
3.have complex theoretical properties
4. Range is sensitive to outliers
5. As n increases range becomes less precise
Computing Std. Dev
1. Measure center as reference point(usu.mean over median)
2. Compute distances from data points to a reference point(x-x bar or mean)
3.Select a representative deviation
Further on std.dev
1. Average of deviation are always zero.(see last mem card)
2.Deviations to the left of mean are negaative
3. See formula for Std.Dev
Steps for calculating std.dev by hand
find x minus mean for each value and square all values.add them up and divide by n minus 1.take square root of ans and u hav it!
Properties of STD.DEV
1.Measures spread around mean (use 's' only when mean is the appropriate center)
2. it is either zero or positive. (s=0 data dont vary)
3.Unit is same as that of observations
4.inflated by outliers
Diff b/w std.dev and variance
Variance: s2:this is average squared deviation from mean.
Std.Dev: s: square root of variance
Population vs Sample (notation for std.dev)
Population:
sigma, meu, N
Sample:
S,x bar,n-1
Why divide by n-1?
1. establish important theoretical properties for inference
2.to make sample variance (S2)an unbiased estimate of population variance(sigma2)
Advantages and Disadvantages of Std.Dev
ADVANTAGES:
1.Commonly used
2.Deiations from every point unlike range and IQR
3.Good theoretical properties
DISADVANTAGES
Inflated by outliers/skewness
Median & IQR (Vs) Mean & Std.Dev
Median & IQR for skewed dis/outliers. (Mean and std.dev affected by outliers/skewed
Symmetrical Dist use mean and std.dev
Rule of thumb
Std.Dev is usually less than one fourth of the range