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Statistics Formulas
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Terms in this set (42)
Class width
(maximum data value) - (minimum data value)
/
Number of classes
Relative Frequency for a class
Frequency of class
/
Sum of all frequencies
Percentage for a class
(Frequency of class
/
Sum of all frequencies)
*
100
Range
(max data value) - (min data value)
minimum usual value
(mean of the data) - 2*(standard deviation of the data)
Maximum usual value
(mean of the data) + 2*(standard deviation of the data)
z-score for a piece of data
[(your piece of data) - (mean of the set of data)] / standard deviation
Mean
∑x/n
Mean of a set of sample values
x-bar=∑x/n
Mean of all values in a population
µ=∑x/N
Mean frequency table
xbar = ∑(f*x)/∑f
Weighted mean
X-bar = ∑(w*x)/∑w
Multiply each weight (w) by the corresponding value (x). The add all the products, and then finally divide that by the sum of the weights, (∑w)
Midrange
Max data value + minimum data values / 2
Median
1. sort the values in order
2. if odd number of values the median is the number located in the exact middle of the sorted list
3. if even number of values the median is found by computing the mean of the two middle numbers in the sorted list.
Standard deviation
s=√∑(x-xbar)²/n-1 (√ extends across all)
Standard deviation (short cut)
s= √n(∑x²)-(∑x)²/n(n-1) (√ extends across all)
Standard deviation (frequency table)
s=√n[∑(f*x²)]-[∑(f*x)]²/n(n-1) (√ extends across all)
Standard deviation estimating a value for s
s≈ range/4
Standard deviation of a population
σ=√∑(x-µ)²/N (√ over all)
Variance
Once you have the standard deviation. simply square the unrounded value from your calculator.
mode
Look for the data value that occurs the most. It is possible to have more than one as long as they occur the same amount of times
Sample variance
s² = square of the standard deviation
Population variance
σ²= square of the population standard deviation
Mean absolute deviation
∑|x-xbar|/n
Chebyshev's Theorem
The proportion (or fractions of any set of data lying within K standard deviations of the mean is always at least 1-1/K², where K is any postive number grater then one. For K=2 and K=3 we get the fallowing statements
At least 3/4 (or 75%) of all values lie within 2 standard deviations of the mean
At lest 8/9 (or 89%) of all values lie within 3 standard deviations of the mean
Coefficient of variation sample
CV=s/x * 100%
Coefficient of variation population
CV=σ/µ * 100%
z score sample
z=x-xbar/s
z score population
z=x-µ/σ
z score usual value
-2≤ z score ≤ 2
Z score unusual value
z score < -2 or z score > 2
Percentile to data value
L=k/100*n
Interquartile range
Q₃-Q₁
Semi-interquartile range
Q₃-Q₁/2
Midquartile
Q₃+Q₁/2
10-90 percentile range
P₉₀-P₁₀
Range rule of thumb for interpreting s
see min and max usual values
Nonstandard normal distribution conversion formula (6-2)
z=x-µ/σ
Nonstandard normal distribution conversion formula (Another form of Formula 6-2)
x=µ+(z*σ)
Probability of success
P(S)=p
Probability of failure
P(F)=1-p=q
Binomial probability formula
n!/(n-x)!x!
*px(power)*qⁿ⁻x(power)
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