# 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 top-notch 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
$$\%=\dfrac{\vert b-a \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100$$ % = % increase or decrease
a = new value
b = original value
c = amount of change

Data Analysis,
Probability,
and Statistics
$$AE=MPV-MV$$
$$RE=\frac{AE}{MV}$$
$$\%E=RE \cdot 100$$
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
$$s=\sqrt{\Sigma(x_i- \overline{x})^2/(n-1)}$$ 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
$$P(x)= \dfrac{n!}{x! \cdot (n-x)!} \cdot p^x \cdot q^{n-x}$$ P(x) = Probability of x successes
p = Probability of success in one trial
q = 1-p = Probability of failure in one trial
n = number of trials
x = number of successes
Binomial Distribution
Formula
Data Analysis,
Probability,
and Statistics
$$P(n,r)=\dfrac{n!}{n-r}!$$ 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
$$C(n,r)=\dfrac{n!}{r! \cdot (n-r)!}$$ C = number of combinations
n = total number of objects in the set
r = number of objects to be chosen from the set