Mean Formula (Arithmetic Mean) The sum of all of the data divided by the count. Piece together the results from Steps 1 and 2 to give you the regression line: y = mx + b. Deborah J. Rumsey, PhD, is a professor of statistics and the director of the Mathematics and Statistics Learning Center at the Ohio State University. Statistics is a branch of mathematics which deals with numbers and data analysis.Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. Sample variance = s2 = Σ ( xi - x )2 / ( n - 1 ) 4. Sample standard deviation = s = sqrt [ Σ ( xi - x )2 / ( n - 1 ) ] 3. } $, Continuous Uniform Distribution - f(x) =$ \begin{cases} This web page lists statistics formulas used in the Stat Trek tutorials. The notation for the mean is. If you come in at the 90th percentile, for example, 90 percent of the test scores of all students are the same as or below yours (and 10 percent are above yours). Take each number and subtract the average from it. For an odd amount of numbers, choose the one that falls exactly in the middle. You’ve pinpointed the median. Divide by the desired margin of error, MOE. These numbers indicate that if this was a room full of children (24 of them), that the average age (the mean) is 5.5 years old.The mode of six would indicate that there are more six-year-old children than any other age in the room. How to remember the standard deviation. Count up all the individuals in the sample who fall into the specified category. For an even amount of numbers, take the two numbers exactly in the middle and average them to find the median. To calculate the test statistic for the sample mean for samples of size 30 or more, you. The median is the middle value after you order the data from smallest to largest. \end{cases} $, Coefficient of Variation -$ {CV = \frac{\sigma}{X} \times 100 } $, Correlation Co-efficient -$ {r = \frac{N \sum xy - (\sum x)(\sum y)}{\sqrt{[N\sum x^2 - (\sum x)^2][N\sum y^2 - (\sum y)^2]}} } $, Cumulative Poisson Distribution -$ {F(x,\lambda) = \sum_{k=0}^x \frac{e^{- \lambda} \lambda ^x}{k!}} Pooled sample standard deviation = sp = sqrt [ (n1 - 1) * s12 + (n2 - 1) * s22 ] / (n1 + n2 - 2) ] 7. After examining a scatterplot between two numerical variables and calculating the sample correlation between the two variables, you might observe a linear relationship between them. Break down the parts of the formula. You can think of it, in general terms, as the average distance from the mean. P (A \cup B) = P(A) + P(B)} $, Probability Multiplicative Theorem -$ {P(A\ and\ B) = P(A) \times P(B) \\[7pt] Formulas — you just can’t get away from them when you’re studying statistics. The formula for the test statistic for the mean is. 0, & \text{when $x \lt a$ or $x \gt b$} is the population standard deviation of all values. {p^x} $, Chebyshev's Theorem -$ {1-\frac{1}{k^2}} $, Circular Permutation -$ {P_n = (n-1)!} In statistics, a confidence interval is an educated guess … The median of a numerical data set is another way to measure the center. Adjusted R-Squared - ${R_{adj}^2 = 1 - [\frac{(1-R^2)(n-1)}{n-k-1}]}$ Arithmetic Mean - $\bar{x} = \frac{_{\sum {x}}}{N}$ Once students understand the math behind a formula, remembering the formula will become easy. The actual number of individuals in any given category is called the frequency for that category. The median is indicated by taking the data set (1,1,1,2,3,4,4,5,5,5,6,6,6,6,6,7,7,7,7,8,8,8,9,9) and counting 12 in from each side. When conducting a hypothesis test for the population mean, you take the sample mean and find out how far it is from the claimed value in terms of a standard score. Round any fractional amount up to the nearest integer (so you achieve your desired MOE or better). But if you understand each part of the formula and how they work together, it can be easier to remember them. Your company has won the rights to 12 leases. Pooled sample proportion = p = (p1 * n1 + p2 * n2) / (n1 + n2) 6. When taking a standardized test, you get an individual raw score and a percentile. For each (x, y) pair in the data set, take x minus. $, Combination with replacement -$ {^nC_r = \frac{(n+r-1)!}{r!(n-1)!} A. {P_1}^{n_1}{P_2}^{n_2}...{P_x}^{n_x}} $, Negative Binomial Distribution -$ {f(x) = P(X=x) = (x-1r-1)(1-p)x-rpr} $, Normal Distribution -$ {y = \frac{1}{\sqrt {2 \pi}}e^{\frac{-(x - \mu)^2}{2 \sigma}} } $, One Proportion Z Test -$ { z = \frac {\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}} } $, Permutation -$ { {^nP_r = \frac{n!}{(n-r)!} Unless otherwise noted, these formulas assume simple random sampling. The formula for the sample size for, where z* is the standard normal value for the confidence level, MOE is your desired margin of error, and. Surveying Statistical Confidence Intervals. 1/(b-a), & \text{when $a \le x \le b$} \\ Each formula is linked to a web page that describe how to use the formula. $, probability -$ {P(A) = \frac{Number\ of\ favourable\ cases}{Total\ number\ of\ equally\ likely\ cases} = \frac{m}{n}} $, Probability Additive Theorem -$ {P(A\ or\ B) = P(A) + P(B) \\[7pt] The mean, or the average of a data set, is one way to measure the center of a numerical data … Users may download the statistics & probability formulas in PDF format to use them offline to collect, analyze, interpret, present & organize numerical data in large quantities to design diverse statistical surveys & experiments. The standard deviation formula is: Standard deviation =sigma=sqrt((Sigma(x-bar x)^2)/(n-1)) 1. Remember, every student is different, their learning capacities are different, and their attention span is different. In general, being at the kth percentile means k percent of the data lie at or below that point and (100 – k) percent lie above it. The standard score is called the test statistic. Subtract the mean (from each number) = x-barx 3. Historically, about 10% of these lands possess sufficient oil reserves for profitable operation. where x represents each of the values in the data set. The mean, or the average of a data set, is one way to measure the center of a numerical data set. Adjusted R-Squared - ${R_{adj}^2 = 1 - [\frac{(1-R^2)(n-1)}{n-k-1}]}$, Arithmetic Mean - $\bar{x} = \frac{_{\sum {x}}}{N}$, Arithmetic Median - Median = Value of $\frac{N+1}{2})^{th}\ item$, Arithmetic Range - ${Coefficient\ of\ Range = \frac{L-S}{L+S}}$, Best Point Estimation - ${MLE = \frac{S}{T}}$, Binomial Distribution - ${P(X-x)} = ^{n}{C_x}{Q^{n-x}}. is an unknown value that you need, you may have to do a pilot study (small experimental study) to come up with a guess for the value of the standard deviation. Unless you have super powers, one look at the formula is not enough to remember it. Use the Z-table to find the corresponding percentile for the standard score. To calculate the median, go through the following steps: Order the numbers from smallest to largest. Square the result (of each of the above) = (x-barx)^2 4. Understand what it indicates. Here are ten statistical formulas you’ll use frequently and the steps for calculating them. Sample mean = x = ( Σ xi ) / n 2. The formula for the standard deviation is. Mean. If you focus on just memorizing the formula, chances are you won't be able to remember it for very long.$, Cohen's kappa coefficient - ${k = \frac{p_0 - p_e}{1-p_e} = 1 - \frac{1-p_o}{1-p_e}}$, Combination - ${C(n,r) = \frac{n!}{r!(n-r)!}} The US land Management Office regularly uses a lottery for the lease of government. 8. Variance of sample proportion = sp2 = pq / (n - 1) 5. Before calculating the regression line, you need five summary statistics: The standard deviation of the x values (denoted sx), The standard deviation of the y values (denoted sy), The correlation between X and Y (denoted r), So, to calculate the best-fit regression line, you. P (AB) = P(A) \times P(B)}$, Probability Bayes Theorem - ${P(A_i/B) = \frac{P(A_i) \times P (B/A_i)}{\sum_{i=1}^k P(A_i) \times P (B/A_i)}}$, Probability Density Function - ${P(a \le X \le b) = \int_a^b f(x) d_x}$, Reliability Coefficient - ${Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ - Sum\ of\ Variance)}{Total Variance})}$, Residual Sum of Squares - ${RSS = \sum_{i=0}^n(\epsilon_i)^2 = \sum_{i=0}^n(y_i - (\alpha + \beta x_i))^2}$, Shannon Wiener Diversity Index - ${ H = \sum[(p_i) \times ln(p_i)] }$, Standard Deviation - $\sigma = \sqrt{\frac{\sum_{i=1}^n{(x-\bar x)^2}}{N-1}}$, Standard Error ( SE ) - $SE_\bar{x} = \frac{s}{\sqrt{n}}$, Sum of Square - ${Sum\ of\ Squares\ = \sum(x_i - \bar x)^2 }$, Trimmed Mean - $\mu = \frac{\sum {X_i}}{n}$, Process Capability (Cp) & Process Performance (Pp).