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# Data Analysis, Statistics, and Probability Formulas for the TSIA2 Assessment

In the TSIA2, you’ll find questions about data analysis, statistics, and probability. These questions actually often involve more “reading” skills than math skills. It sounds counterintuitive, but it’s true. The #1 skill you need for solving these problems is reading and understanding the problem and the data you have. After that, you just need to compute and apply the proper formula, and to help you with that we have compiled the essential formulas you’ll need for the Data Analysis, Statistics, and Probability problems. Just see the chart, below.

You’ll also want to check out our other two math formula charts for this test:

Formulas for Algebra and Functions

Formulas for Geometry and Measurement

And for practice using these formulas and the ones in our other TSIA2 charts, try our free TSIA2 test prep.

## Data Analysis, Statistics, and Probability Formulas

Category Formula Symbols Comment
Data
Analysis
Statistics and
Probability
$$Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF$$ Du = Desired Unit
Su = Starting Unit
CF = Conversion Factor
Multiple steps may
be needed.
Data
Analysis
Statistics and
Probability
$$a \cdot b\% =a \cdot \frac{b}{100}$$ a = any real number
b% = any percent
Remember to simplify
if necessary
Data
Analysis
Statistics and
Probability
$$\% = \frac{\vert b-a \vert }{b} \cdot 100= \frac{c}{b} \cdot 100$$ % = % increase or decrease
a = new value
b = original value
c = amount of change

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

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

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

Data
Analysis
Statistics and
Probability
$$Q1=\frac{1}{4}(n+1)^{th}$$ term
$$Q2= Q3 - Q1$$
$$Q3= \frac{3}{4}(n+1)^{th}$$ term
Q1 = Lower Quartile
Q2 = Middle Quartile
Q3 = Upper Quartile
n = number of measurements

Data
Analysis
Statistics and
Probability
$$s=\sqrt{\Sigma(x_i-\overline{x})^2/(n-1)}$$ s = standard deviation
$$\overline{x}$$ = mean
$$x_i$$ = value of each measurement
n = number of measurements

Data
Analysis
Statistics and
Probability
$$V=s^2$$ v = Variance
s = standard deviation

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

Data
Analysis
Statistics and
Probability
$$p = \dfrac{d}{t}$$ p = probability of an event
d = number of times the desired event can occur
t = total number of events