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Business Stats - Formulas (1 - 4)
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Business Statistics in Practice (Bowermand, OConnell, Murphree), ed 6
Terms in this set (22)
assigning probabilities: Classical Method
P(A) = (total # of times A occured) / (total # of sample space outcomes)
assigning probabilities: Relative Frequency
P(an event) = (# of times an event occured) / (total # of opportunites for the event to occur)
Complement of an Event
P(A) + P(A^c) = 1
Addition Rule
P(A or B) = P(A) + P(B) - P(A and B)
Conditional Probability
P(A | B) = P(A and B) / P(B)
P(B) > 0
Independent Events
P(A | B) = P(A)
Multiplication rule
Independent:
P(A and B) = P(A) x P(B)
Dependent:
P(A and B) = P(A) x P(B | A)
P(A and B) = P(B) x (P(A | B)
Fundamental Counting Rule
For a sequence of two events in which the first event occurs in m ways and the second event occurs in n ways for a total of m x n ways (this can be applied to more than two events)
Permutations
nPr = n! / (n-r)!
Requirements for using the below formula
- There are n different items
- We select r of the n items (without replacement)
- Rearrangements of the items are different sequences
Combinations
cCr = n! / (n-r!)r!
Requirements for using the below formula
- There are n different items
- We select r of the n items (without replacement)
- Rearrangements of the items are the same
sample mean
x-bar = Σx / n
n = total # of data values in the sample
population mean
μ = Σx / N
N = total # of data values in the population
weighted mean
X-bar = (w1X1 + ... + wnXm) / ( w1 + ... + wn)
= Σ(wX)/Σ(w)
sample variance
s^2 = Σ(x - xbar)^2 / (n - 1)
n = total # of data values in the sample
sample standard deviation
s = SQR (Σ(x - xbar)^2 / (n - 1))
n = total # of data values in the sample
population variance
σ^2 = Σ(1-μ)^2 / N
N = total # of data values in the population
populatin standard deviation
σ = SQR (Σ(1-μ)^2 / N)
N = total # of data values in the population
coefficient of variation (CV)
CV = 100 x s/x-bar
= 100 x σ/μ
Interquartile Range (IQR)
IQR = Q3 - Q1
Lower Fence
Inner Fence:
Q1 - 1.5(IQR)
If a data point falls outside of the inner fence then it is considered a mild outlier
Outer Fence:
Q1 - 3.0(IQR)
If a data point falls outside of the outer fence then it is considered an extreme outlier
Upper Fence
Inner Fence:
Q3 +1.5(IQR)
If a data point falls outside of the inner fence then it is considered a mild outlier
Outer Fence:
Q3 + 3.0(IQR)
If a data point falls outside of the outer fence then it is considered an extreme outlier
Histogram
Determine the number of classes:
**If the number of classes is not given to you we can find the number of classes by identifying the smallest whole number K that makes the quantity 2Kgreater than the total number of observations in the data set.
Determine the class length:
- class length = (max value -min value) / # of classes
Obtain class boundaries
- Lower Class Boundary of first class = minimum data value in data set.
- Upper Class Boundary of first class = Lower Class Boundary + Class Length
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