Exam Pointers:● Skewness based on mean and median● Mean < median: left skew● Mean > median: right skewCh1 &2Location parameters● Mean (μ): mean(xi)= 1N ∑i=1Nxi○ Scaling and translating: mean(a{xi+c })=a⋅mean({xi})+c○ ∑i=1N(xi-mean({xi}))=0○xi-μ¿2¿^ μ=mean({xi})=argm¿μ∑i=1N¿○ Mean and standard deviation are very sensitive to outliers.● Median:○ Not sensitive to o
...[Show More]
Exam Pointers:
● Skewness based on mean and median
● Mean < median: left skew
● Mean > median: right skew
Ch1 &2
Location parameters
● Mean (μ): mean(xi)= 1
N ∑i=1
N
x
i
○ Scaling and translating: mean(a{xi+c })=a⋅mean({xi})+c
○ ∑
i=1
N
(xi-mean({xi}))=0
○
xi-μ¿2
¿
^ μ=mean({xi})=argm¿μ∑
i=1
N
¿
○ Mean and standard deviation are very sensitive to outliers.
● Median:
○ Not sensitive to outliers. Same applies to IQR.
○ median({k ⋅ xi+c})=k ⋅median({xi})+c
● Mode:
○ Peaks in a histogram. If there’s more than one peak, we should be curious as to
why.
Scale parameters
● Standard deviation (σ): std({xi})=√❑ = √❑
○ Standard deviation of a dataset cannot be -1
https://www.coursehero.com/file/72636308/CS-361-Midterm-1-Cheat-Sheet/
This study resource was
shared via CourseHero.com
○ Scaling and translation: std({k⋅ xi+c })=¿ k∨⋅ std({xi})
○ Chebyshev’s Inequality:
■ At most
N2k
items are k standard deviations (σ) away from the mean
● Variance (σ2) = (standard deviation)2:
xi-mean({xi})¿2
¿
var ({xi})= 1
N ∑
i=1
N
¿
● Interquartile range (IQR):
○ IQR is used to find a summary that describes scale, but is less affected by
outliers than the standard deviation.
○ Quartiles:
■ First quartile: Value in which 25% of data <= that value (percentile({x},
25))
■ Second quartile: Value such that 50% of data <= value (usually median)
■ Third quartile: 75%; percentile({x}, 75)
○ IQR{x} = percentile({x}, 75) - percentile({x}, 25)
○○
How to calculate percentile:
■ Rank the values in the data set in order from smallest to largest
■ Multiply k (percent) by n
[Show Less]
-preview.jpeg)
-preview.jpeg)
-preview.jpeg)
