# Formula Chart for Statistics and Probability on the SBAC Test

These days, statistics is getting more and more important. A lot of things, from Google search results to the ads you see on the Internet, are based on statistics. Do you want to understand how these work, and also ace the SBAC Test? You have to start from the basics. In the following chart, you’ll find the essential Statistics and Probability formulas you’ll need to solve problems on the SBAC Test. Even though you’re not going to be able to use the chart during the actual test, it will help you study and prepare for it! Use it to solve the sample problems at Union Test Prep!

And don’t forget to check out the other charts about 11th-grade math on the SBAC:

Algebra

Functions

Geometry

Number and Operations

## Formulas for Statistics and Probability

Category Formula Symbols Comment
Statistics $$\overline{x} = \dfrac{\Sigma x_i}{n}$$ $$\overline{x}$$ = sample mean
$$x_i$$ = value of each measurement
$$n$$ = number of measurements

Statistics $$\mu = \dfrac{\Sigma x_i}{N}$$ $$\mu$$ = population mean
$$x_i$$ = value of each measurement
$$N$$ = number of items in the population

Statistics $$Md = (\frac{n+1}{2})^{th} \ term$$ $$Md$$ = Median
$$n$$ = number of measurements (odd)

Statistics $$Md = \dfrac{(\frac{n}{2})^{th} \ term + (\frac{n}{2} +1)^{th} \ term}{2}$$ $$Md$$ = Median
$$n$$ = number of measurements (even)

Statistics $$Q_1 = \frac{1}{4} \cdot (n+1)^{th} \ term$$
$$Q_2 = \frac{2}{4} \cdot (n+1)^{th} \ term$$
$$Q_3 = \frac{3}{4} \cdot (n+1)^{th} \ term$$
$$Q_1$$ = Lower Quartile
$$Q_2$$ = Middle Quartile
$$Q_3$$ = Upper Quartile

Statistics $$IQR = Q_3 - Q_1$$ $$IQR$$ = Interquartile Range
$$Q_1$$ = Lower Quartile
$$Q_3$$ = Upper Quartile

Statistics $$rg = lv - sv$$ $$rg$$ = range
$$lv$$ = largest value in the data set
$$sv$$ = smallest value in the data set

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

Statistics $$V = s^2$$ $$V$$ = Variance
$$s$$ = Standard Deviation

Statistics $$CV = RSD = 100 \cdot \frac{s}{\overline{x}}$$ $$CV$$ = Coefficient of Variation
$$RSD$$ = Relative Standard Deviation
$$s$$ = Standard Deviation
$$\overline{x}$$ = mean

Statistics $$r_i = y_i -\hat{y_i}$$ $$r_i$$ = Residual
$$y_i$$ = Observed Value
$$\hat{y_i}$$ = Predicted Value

Statistics $$r_{xy} = \dfrac{\displaystyle\sum_{i=1}^{n}(x_i-\overline{x}) \cdot (y_i-\overline{y})}{\sqrt {\displaystyle\sum_{i=1}^{n}(x_i-\overline{x})^2 } \cdot \sqrt {\displaystyle\sum_{i=1}^n(y_i-\overline{y})^2}}$$ $$r_{xy}$$ = Pearson’s Correlation Coefficient
$$x_i, y_i$$ = Individual Sample Points indexed with i
$$n$$ = Sample Size
$$\overline{x}$$ = Sample Mean For x
$$\overline{y}$$ = Sample Mean For y

Probability $$p= \frac{d}{t}$$ $$p$$ = Probability of an Event
$$d$$ = Number of Ways Desired Event Can Occur
$$t$$ = Total Number of Possible Events

Probability $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ $$P(A \cup B)$$ = Probability of A or B
$$P(A)$$ = Probability of A
$$P(B)$$ = Probability of B
$$P(A \cap B)$$ = Probability of A and B
Probability $$P(A \cap B) = P(A) \cdot P(B)$$ $$P(A \cap B)$$ = Probability of A and B
$$P(A)$$ = Probability of A
$$P(B)$$ = Probability of B
Probability $$P(A \cap B) = 0$$ $$P(A \cap B)$$ = Probability of A and B Mutually Exclusive Events