Important Data Analysis, Probability, and Statistics Formulas to Know for the ISEE Math Tests
To ace the Data Analysis, Probability, and Statistics questions on the two math tests on the ISEE, you need to be very careful! Questions of this type require topnotch accuracy, so you need to be able to select the appropriate formula for each problem. Union Test Prep has prepared charts of formulas for the 4 different areas of math. Our three other charts are linked here:
The chart below contains formulas for the area of Data Analysis, Probablility, and Statistics— the one with which you need to be the most careful. Be sure to practice the use of these equations by solving the free problems we have for you in our Mathematics Achievement and Quantitive Reasoning practice tests.
Data Analysis, Probability, and Statistics Formulas for the ISEE Math Tests
Category  Formula  Symbols  Comment 

Data Analysis, Probability, and Statistics 
\(Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF\)  Du = Desired Unit Su = Starting Unit CF = Conversion Factor 
Multiple steps may be needed. 
Data Analysis, Probability, and Statistics 
\(a \cdot B\%=a \cdot \dfrac{b}{100}\)  a = any real number b% = any percent 
Remember to simplify if possible 
Data Analysis, Probability, and Statistics 
\(\%=\dfrac{\vert ba \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100\)  % = % increase or decrease a = new value b = original value c = amount of change 

Data Analysis, Probability, and Statistics 
\(AE=MPVMV\) \(RE=\frac{AE}{MV}\) \(\%E=RE \cdot 100\) 
AE = Absolute Error MPV = Maximum Possible Value MV = Measured Value RE = Relative Error %E = Percentage Error 

Data Analysis, Probability, and Statistics 
\(\overline{x}=\dfrac{\Sigma x_i}{n}\)  \(\overline{x}\) = mean \(x_i\) = value of each measurement n = number of measurements 

Data Analysis, Probability, and Statistics 
\(Md=(\dfrac{n+1}{2})^{th}\ term\)  Md = Median n = number of measurements (odd) 

Data Analysis, Probability, and Statistics 
\(Md=\dfrac{(\frac{n}{2})^{th} term + (\frac{n}{2}+1) ^{th} term}{2}\)  Md = Median n = number of measurements (even) 

Data Analysis, Probability, and Statistics 
\(s=\sqrt{\Sigma(x_i \overline{x})^2/(n1)}\)  s = standard deviation \(\overline{x}\) = mean \(x_i\) = value of each measurement n = number of measurements 

Data Analysis, Probability, and Statistics 
\(V=s^2\)  V = Variance s=standard deviation 

Data Analysis, Probability, and Statistics 
\(CV=RSD=100 \cdot \dfrac{s}{\overline{x}}\)  CV = Coefficient of variation RSD = Relative standard deviation s = standard deviation \(\overline{x}\) = mean 

Data Analysis, Probability, and Statistics 
\(P(A \cup B)=P(A)+P(B)P(A \cap B)\)  \((A \cup B)\) = Probability of A or B P(A) = Probability of A P(B) = Probability of B \(P(A \cap B)\)=Probability of A and B 
Rule of Addition 
Data Analysis, Probability, and Statistics 
\(P(A \cap B)=P(A) \cdot P(B)\)  \(P(A \cap B)\) = Probability of A and B P(A) = Probability of A P(B) = Probability of B 
Independent Events 
Data Analysis, Probability, and Statistics 
\(P(A \cap B)=0\)  \(P(A \cap B)\)=Probability of A and B  Mutually Exclusive Events 
Data Analysis, Probability, and Statistics 
\(P(A \vert B)= \dfrac{P(A \cap B)}{P(B)}\)  \(P(A \vert B)\) = Probability of A given B P(A \cap B) = Probability of A and B P(B) = Probability of B 
Conditional Probability 
Data Analysis, Probability, and Statistics 
\(P(B \vert A)= \dfrac{P(A \vert B) \cdot P(B)}{P(A)}\)  \(P(B \vert A)\) = Probability of B given A \(P(A \vert B)\) = Probability of A given B P(B) = Probability of B P(A) = Probability of A 
Bayes’ Theorem 
Data Analysis, Probability, and Statistics 
\(P(x)= \dfrac{n!}{x! \cdot (nx)!} \cdot p^x \cdot q^{nx}\)  P(x) = Probability of x successes p = Probability of success in one trial q = 1p = Probability of failure in one trial n = number of trials x = number of successes 
Binomial Distribution Formula 
Data Analysis, Probability, and Statistics 
\(P(n,r)=\dfrac{n!}{nr}!\)  P = number of permutations n = total number of objects in the set r = number of objects to be chosen from the set 

Data Analysis, Probability, and Statistics 
\(C(n,r)=\dfrac{n!}{r! \cdot (nr)!}\)  C = number of combinations n = total number of objects in the set r = number of objects to be chosen from the set 
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