top of page

# Formula Library

Formulas and tables are used to calculate values and compare data. Formulas are mathematical expressions that contain variables, constants, and operators. The most common formula is a linear equation that uses one variable, such as y = 2x - 4 or y = (x + 3)2. Formulas can also include functions that return values for different inputs, such as sin(4π) or log(x). The following table shows the common notation used in formulas and tables.

X-bar and range

In a data set, the difference between the highest and lowest values is called the range. The average of these two values across all samples in that data set is called X-bar (pronounced "X bar"). This can be calculated as:

Show the following table:

A B C D E

2 2 6.5 6.5 7.5 11.5

3 2.5 4.5 7.5 10.5 14

Samplesize A B C D E

You can use the SAMPLESIZE formula to determine the sample size needed to detect a difference between two population means.

For example, let’s say you are sampling a group of people and want to know if they will be able to spot a difference in heights between men and women at different ages. You could use the SAMPLESIZE formula as follows:

A = 1,000 B = 0 C = 10 D = 10 E =

2 2 6.5 6.5 7.5 11.5

To find the average and range of a set of numbers, use the following formula:

Average = sum of all values / number of values in the set

Range = maximum value - minimum value. The formula for finding the standard deviation, or how much variation there is from one data point to another in a set of numbers is:

Standard Deviation = square root ((sum(squared deviations))/number of values) x 2. The coefficient of variation (CV) is calculated by dividing the standard deviation by an individual data point's mean squared deviation from its mean as this represents how "spread out" or diverse a dataset is from its mean value when compared to other datasets. CV can be used as an indicator for determining whether or not outliers exist within your sample data sets if they are outside one standard deviation above or below their respective means; however, it's not necessarily accurate at predicting which points are truly outliers because it fails if there aren't enough samples available to calculate confidence intervals around each individual's average score (which would make up most statistical analyses).

3 2.5 4.5 7.5 10.5 14

The average of 2.5 and 4.5 is 3.5

The median of 2, 6, 7, 10 and 14 is 7.5

The mode of 2,6,7and 10 is 14

The range is 7.5-2.5 = 5

4 3.5 7.5 11.5

The mean, median and mode are all measures of central tendency.

The mean (average) is the sum of all data points divided by the number of data points.

The median is the middle value when arranged from smallest to largest value.

The mode is the most frequent value or values in a distribution (data set). If there are no repeated values, then there is no mode for that distribution.

5+4*sqrt(n)<50 3.75 9 14

5+4*sqrt(n)<50 3.75 9 14

75 is the median, which means that half of all values are lower than it and half are higher

9 is the sigma, which is a measure of how much variation there is around the mean (the average value)

14 is the mean

Conclusion