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# Statistical Formula

Statistics is the branch of mathematics that deals with the analysis of data. Statistical methods are developed to analyze the large volumes of data and their properties. Statistical methods are used by many organizations to calculate a collaborative property about employees or people. In this article, we will discuss various statistical formula. Let us learn the concept.

## Statistical Formula

### What is statistics?

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of the large data. The statistical theory defines a statistic as a function of the sample data where the function itself is independent of the sample’s distribution.

Therefore, Statistics is associated with collecting, classifying, arranging and presenting the numerical data related in some context. It also allows us to interpret many results from it and forecast many possibilities for further applications. Using statistics, we can find various measures of central tendencies and the deviation of different values from the center.

### The formula in statistics:

For almost all statistical computations, the basic concepts of mean, median, mode, variance, and standard deviation are the stepping stones.

(1) Mean or Average:

Mean in theory is defined as the sum of all the elements of a set divided by the number of elements. We can get a fairly good idea about the whole set of data by calculating its mean. Thus the formula for mean is:

Mean = $$\frac{Sum of all the set elements} {Number of elements}$$

The importance of mean lies in its ability to represent the whole dataset with a single value.

(2) Median:

Median is the middle value of a dataset. So, if a set consists of an odd number of values, then the middle value will be the median of the set. On the other hand, if the set consists of an even number of sets, then the median will be the average of the two middle values.

Thus, the median may be used to separate a set of data into two parts. To find the median of a set, we need to arrange the elements of the set in increasing order. Then find the middle value.

(3) Mode:

The mode in a dataset is the value that is most frequent in the dataset. The mode also summarizes the gdataset with single information.

(4) Variance:

We may want to measure the deviation of a set of data from their mean value. The variance of the particular dataset will always be positive. Variance is used in the calculation of Standard Deviation, which is a very important concept of statistics.

(5) Standard Deviation:

The standard deviation is defined as the square rooting of the variance of the data.

### Statistics Formula Sheet:

 Mean $$\bar X = \frac{\sum x}{n}$$ $$\bar X = mean value$$ x = Items given n = Total number of items Median If n is odd, then M = $$\frac{n+1}{2}$$th term If n is even, then M = $$\frac {\frac{n}{2}th \;term + (\frac{n}{2}+1)th\; term}{2}$$ M = median value n = Total number of items Mode The value which occurs most frequently Variance $$\sigma^2=\frac{\sum {(x-\bar x)}^2}{n}$$ $$\sigma ^ 2 = variance$$ x = Items given $$\bar X = Mean$$ n = Total number of items Standard Deviation $$S= \sigma$$ $$\sigma^ 2 = variance$$ S = Standard Deviation

## Solved Example

Q: Find the mode of the set S = 1,2,3,3,3,3,3,4,4,4,5,5,6,7.

Solution: Here 3 occurs maximum 5 times. Therefore 3 is the mode.

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