Central tendency summarizes an entire data set with a single value – often represented by the mean, median, and mode. In statistics, they are the foundation of numerical analysis. This guide explains how to compute mean, median, and mode in R.

## Mean

The mean is used to find the average of the data or dataset. It is the summation of all the numbers in the dataset divided by the number of observations. There are two methods to calculate the mean in R.

### Method 1: Using the mean() function

**mean()** is a function built-into R.

#### Syntax

`mean(x)`

#### Argument

- x = numerical vector

#### Example: Calculating the mean of a vector using the mean() function

```
#creating a vector
x <- c(21,21,22.8,21.4,18.7,18.1,14.3,24.4)
#calculating mean
mean(x)
```

#### Output

`[1] 20.2125`

### Method 2: Using the sum() and length() functions

Mathematically, the mean is calculated by adding all the numerical values in the dataset divided by the number of data in it.

#### Syntax

`sum(x)/length(x)`

#### Arguments

- x = numerical vector
- sum = built-in function to compute the sum of all the values in a vector
- length = built-in function to find the number of observations in a vector

#### Example: Calculating the mean of a vector using the sum() and length() function

```
#creating a vector
x <- c(21,21,22.8,21.4,18.7,18.1,14.3,24.4)
#calculating mean
x_mean <- sum(x)/length(x)
x_mean
```

#### Output

`[1] 20.2125`

## Median

The median is the middlemost value in a dataset arranged in ascending order. To calculate the median in R, use the **median()** function.

#### Syntax

`median(x)`

#### Argument

- x = numerical vector

#### Example: Calculating the median of a vector in R

```
#creating a vector
x <- c(12,15,23,25,27,13,14,15,15)
#calculating median
median(x)
```

#### Output

`[1] 15`

## Mode

Mode is the most frequent data in a data set. It is mainly applied to a dataset containing nominal data like **Yes** or No. To compute the mode in R, use the **mlv()** function.

### Installation

The mlv() function is built into the **Modeest** package. To install and load the package, run the following code:

```
install.packages(“modeest”)
library(“modeest”)
```

#### Syntax

`mfv(x, method)`

#### Arguments

- x = a vector
- method = returns the most frequent value in a vector

#### Example: Calculating the mode of a vector in R

```
#creating a numerical vector
x <- c(12,15,23,25,27,13,14,15,15)
#creating a string vector
y <- c('ryan','mary','edwards','mary','erica','mary')
#calculating mode
mlv(x, method = 'mfv') #mode of vector x
mlv(y, method = 'mfv') #mode of vector y
```

#### Output

```
[1] 15
[1] "mary"
```