Statistics + Formula Logic

Average =

(Sum of terms) / (# terms)

Sum of terms =

(Avg. of terms) * (# terms)

If set of C terms is comprised of subset of A terms and subset of B terms, then the sum of all C terms is…

A_Q x Avg_A + B_Q x Avg_B = (A+B)_Q x Avg_Total = Sum of all C terms

Count of consecutive integers inclusive of the endpoints

Highest - Lowest + 1

Count of consecutive even/odd integers in a set, inclusive of end points

(Highest odd/even - lowest odd/even) / 2 + 1

Count of multiples of x in a given set, inclusive of endpoints

[(Highest Mult of X - Lowest Mult of X) / X] + 1

Count of consecutive integers inclusive of one endpoint but not both

Highest number - lowest number

Count of consecutive integers between two endpoints / exclusive of both

Highest - Lowest - 1

Average of an evenly spaced set

(Highest + Lowest) / 2

Number of multiples of A or B in a set of consecutive integers

(# of Mults of A) + (# of Mults of B) - (#Number of Mults of LCM(A,B))

Number of multiples of A or B in a set of consecutive integers, but not both

(# of Mults of A) + (# of Mults of B) - 2 x (#Number of Mults of LCM(A,B))

Weighted Average

[(A x Frequency of A) + (B x Frequency of B)] / (Total Frequency of A&B)

Position of the median in a set of n terms, where n is odd

(n+1)/2

Position of the median in a set of n terms, where n is even

Avg. of terms at n/2 and (n+2)/2 positions

If we have an equally spaced set, the mean =

the median

Finding the minimum range when combining two or more sets

Min range for the combined set is the greater of the ranges of the subsets

Greatest possible range when combining two or more sets

Greatest possible value - the lowest possible value of the combined set

If the standard deviation of {a,b,c,} is n, what is the std dev of {a±k, b±k, c±k}

n

If the standard deviation of {a,b,c,} is n, what is the std dev of {10a, 10b, 10c}

10n

Adding a number equal to the mean of the set will…

decrease the Std Dev closer to 0

Comparing Std Deviations without fully calculating (must be equal # of terms)

1. Determine the mean of each set

2. Determine the absolute difference between the mean and each data point

3. The set with greatest sum of absolute differences has the greatest Standard Deviation

If standard deviation of a set equals zero…

…then all of the terms are the same / equal the mean

If the range of a set equals zero…

…then all of the terms are the same / equal the mean

If the min or max of a set equals the mean…

…then all of the terms are the same / equal the mean

How to calculate a range for a sum of consecutive reciprocals?

1. Calculate the number of terms

2. Multiply the number of terms by the min and max reciprocal to calculate range end points

If M is being increased by a factor of f, new value equals…

if f >= 1: Mf

if f < 1: M + mf

If M is being decreased by a factor of f, new value equals…

if f >= 1: Mf

if f < 1: M - mf