Calculate the Arithmetic, The mean of a data set is derived by dividing the total of all data sets by the number of observations in the data set.

### Calculate the Arithmetic:

The __mean formula__ is the most popular and widely used approach in statistics for determining the center of data collection. It’s a basic, yet crucial, element of statistical data analysis. The population means is what we get when we compute the average value of a population set. We sometimes can’t conduct any analysis on population data since it’s too vast. As a result, in such a scenario, we take a sample and average it. That sample represents the population, and the sample mean is the average of this part of the dataset.

Mean=

It’s worth noting that the mean value is the average value in the data set, which will lie between the maximum and minimum values. The mean value will not be the same as the data set’s value, but its values are occasionally the same.

## Mean Formula for Ungrouped Data

The formula to find the mean of ungrouped data is given below:

Here,

= ith observation

∑ = Sum of observations

n = Number of observations

## Mean Formula for Grouped Data

They are:

- Direct Method
- Assumed Mean Method
- Step-deviation Method

### ● Direct Method

Assume that ,…., are n observations, each with a frequency of , ,…., . This indicates that happens times, happens times, and so on. the formula to calculate mean by the direct mean method is shown below:

Here,

∑ = Sum of all the observations

∑ = Sum of frequencies or observations

Thus, the formula to find the mean in the assumed mean method is:

Here,

a = assumed mean

= frequency of ith class

= – a = deviation of ith class

Σ = N = Total number of observations

= class mark = (upper class limit + lower class limit) / 2

### ● Step-Deviation Method

The formula is given by:

Here,

a = assumed mean

= frequency of ith class

– a = deviation of ith class

= ( – a)/h

Σ = N = Total number of observations

= class mark = (upper class limit + lower class limit) / 2

## Measures Of Central Tendency

The statistical metric that captures the single value of the whole distribution or dataset is referred to as the __measures of central tendency__. Its goal is to offer a complete explanation of the distribution’s data.

Mean, median, and mode is used to find the central tendency of the dataset.

- Mean

The average value of the dataset is represented by the mean. It may be determined by dividing the total of all the values in the dataset by the number of values. It is commonly referred to as the arithmetic mean. - Median

The median value of a dataset, whether it is sorted in ascending or descending order, is the dataset’s middle value. When there are an even number of items in a dataset, the median value may be calculated by taking the mean of the middle two values. - Mode

The mode reflects the value that appears most frequently in the dataset. There are times when the dataset has numerous modes and other times when it contains none at all.

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