When Should You Take the SAT? Full Guide to Choosing 2025

Standard deviation is the square root of the variance.

The range is $a-b$, where $a$ is the largest value, and $b$ is the smallest.

This formula simplifies the calculation of variance.

When dealing with grouped data (data organized into intervals or classes), you use the midpoint of each class interval to represent all the values within that interval. You multiply each midpoint (x) by its corresponding frequency (f), sum these products (∑f * x), and then divide by the total frequency (∑f).

The median class is the class that contains the N/2-th value. Therefore, the cumulative frequency up to the median class represents the number of values before the median class and is equal to N/2

Variance is the square of the standard deviation.

Standard deviation measures the spread of data points from the mean.

To find the mean of any set of numbers, you add them together and divide by the count of those numbers. In this case, there are three numbers (a, b, and c), so you add them and divide by 3.

If every value in a dataset is multiplied by a constant (k), the mean of the new dataset will also be multiplied by that same constant.

This is the shortcut formula for calculating standard deviation for grouped data.

This is the standard formula for calculating sample standard deviation.

Observations refer to the data points in a dataset, and range is the difference between the largest and smallest observations.

The range is the difference between the highest and lowest values in a dataset.

The weighted mean takes into account the "weight" or importance of each value. It's calculated by multiplying each value (x) by its weight (w), summing these products (∑wx), and then dividing by the sum of the weights (∑w).

The mode is the value that appears most often in a dataset.  

• Arrange the data in ascending order: 2, 3, 5, 7, 10
• Since there are 5 data points (an odd number), the median is the middle value, which is 5.

In a grouped frequency distribution, boundaries are used to calculate the range.

Standard deviation is the square root of the variance.

N represents the total number of individuals in the population.

If no value repeats, there is no single "most frequent" value, so the dataset has no mode. Some might say it's undefined, but "no mode" is the more common and accurate term.

This is another common and slightly simplified version of the grouped data mode formula. The variables are the same as in question 1:

• L = Lower class boundary of the modal class  
• f_m = Frequency of the modal class  
• f₁ = Frequency of the class preceding the modal class  
• f₂ = Frequency of the class succeeding the modal class  
• h = Class width  

Class boundaries (not midpoints) are used to calculate range for grouped data.

Grouped data uses class boundaries to calculate range.

Range is the difference between the highest and lowest values.

U is the largest value, and L is the smallest value of the dataset.

Variance is the square of the standard deviation.

Range is always the difference between the maximum (a) and minimum (b).

Relative range is the range divided by the mean of the dataset.

Variance is the average of the squared deviations from the mean.

Range is the difference between the maximum and minimum values.

$a$ and $b$ represent maximum and minimum values, respectively.

This is the shortcut formula for calculating standard deviation directly from the raw data.

This is the formula for sample standard deviation.

This shortcut method simplifies calculations when dealing with large datasets.

This formula uses the population mean (μ) and the population size (N).

Range in grouped data is calculated using class boundaries.

This formula accounts for the frequencies of each data point in grouped data.

CV measures the relative dispersion of data.

Range is calculated as the difference between the maximum and minimum values of the dataset.

• L = Lower class boundary of the median class
• N = Total frequency
• F = Cumulative frequency before the median class
• f_m = Frequency of the median class
• h = Class width

When you have an odd number of data points, the median is the middle value after arranging the data in ascending or descending order. The formula (n+1)/2 gives you the position of that middle value.

Continuous data uses boundaries for range calculation.

When you have an even number of data points, the median is the average of the two middle values after arranging the data in order.

$L$ stands for the Largest (or maximum) value in the dataset.

Range is the difference between the maximum and minimum values.

This is the standard formula for calculating the mode in a grouped frequency distribution:

• L = Lower class boundary of the modal class (the class with the highest frequency)  
• f_m = Frequency of the modal class  
• f₁ = Frequency of the class preceding the modal class  
• f₂ = Frequency of the class succeeding the modal class  
• h = Class width  

This formula accounts for the frequencies of each data point in grouped data.

This formula accounts for the frequencies of each data point in grouped data.

Sample standard deviation uses (n-1) in the denominator to provide an unbiased estimate.

The arithmetic mean (or average) is calculated by adding up all the values in a dataset and then dividing by the total number of values.

$U$ is the Upper Limit and $L$ is the Lower Limit in a frequency distribution.

Range is the difference between maximum and minimum values.

Sample standard deviation uses (n-1) in the denominator to provide an unbiased estimate.

$R=\text{Maximum Value}-\text{Minimum Value}$ is the most basic form of the range formula.