Statistics Formula

The discipline concerning the compilation, organization, study, interpretation, and presentation of data is statistics. It is traditional to start with a statistical population or a statistical model to be studied when applying statistics to a scientific, industrial, or social problem. It also helps us to explain many observations from it and foresee many possibilities for additional applications. We may find various measurements of central tendencies and the divergence of different values from the centre using statistics.

What Are the Various Statistics Formulas?

The Main Concepts in Statistics Are 

• Mean

• Median

• Mode

• Standard deviation

• Variance

Let Us Understand the Above 5 Statistics Formulas With Examples : 

• 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.

• 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.

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• Mode: The mode is the value that most frequently appears in a data value set.

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• Standard Deviation: A calculation of the amount of variance or dispersion of a set of values is the standard deviation.

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• Variance: The expectation of the square deviation of a random variable from its mean is variance.

Now let us look at the formula of statistics that can be used while solving the problems.

Basic Statistics Formulas

To solve statistical problems, there are few formulas of statistics that will be used the most, they are as follows :

• Mean: To calculate the mean of a given data set, we use the following formula, 

Mean (\[\bar{x}\]) = \[\frac{\sum x}{N}\]

• Median: 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, 

Median = \[(\frac{n+1}{2})^{th}\] observation

If an even number of terms are given in the data set, we use the following formula, 

Median = \[\frac{(\frac{n}{2})^{th} \; observation + (\frac{n}{2}+1)^{th} \; observation}{2}\]

• Mode: 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.

Mode =  \[l + (\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}) \times h\]

• 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.

Standard deviation(𝜎) = \[\sqrt{\frac{\sum (x_{i}-\mu)^{2}}{N}}\]

• 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).

Variance(𝜎2) = \[\frac{\sum (x_{i}-\mu)^{2}}{N}\]

These are a few formulas for statistics that are to be used while attempting any statistics problems. 

Conclusion

In statistics, the aim is to gather and analyze vast amounts of numerical data, in particular for the purpose of deducting the proportions in total from those in the representative sample. In statistics, all formulas are given in data sets on which the analysis is done.