Important Formulas: Statistics | Quantitative for GMAT PDF Download

Statistics is a mathematical field focused on numbers and the analysis of data. It involves the examination, interpretation, presentation, and arrangement of data. Within statistical theory, a statistic is defined as a function applied to a sample, and this function remains unaffected by the distribution of the sample.

The important statistics formulas are listed in the chart below:

1. Mean: 

• The arithmetical mean is the sum of a set of numbers separated by the number of numbers in the collection, or simply the mean or the average. 
• To calculate the mean of a given data set, we use the following formula,
  

2. Median: 

• In a sorted, ascending or descending, list of numbers, the median is the middle number and may be more representative of that data set than the average. 
• In the case of the median, we have two different formulas. If we have an odd number of terms in the data set  we use the following formula,
  
• If an even number of terms are given in the data set, we use the following formula,
  

3. Mode: 

• The mode is the value that most frequently appears in a data value set. 
• In the case of clustered frequency distributions, it is not possible to calculate the mode simply by looking at the frequency. We measure the modal class in order to evaluate the data mode in such situations. Inside the modal class, the mode lies.
  

4. Standard Deviation: 

• A calculation of the amount of variance or dispersion of a set of values is the standard deviation. 
• By evaluating the deviation of each data point relative to the mean, the standard deviation is calculated as the square root of variance.
  

5. Variance: 

• The expectation of the square deviation of a random variable from its mean is variance.
• The variance is defined as the total of the square distances from the mean (μ) of each term in the distribution, divided by the number of distribution terms (N).