Variability in R Programming - GeeksforGeeks

10 May, 2020
Variability (also known as Statistical Dispersion) is another feature of descriptive statistics. Measures of central tendency and variability together comprise of descriptive statistics. Variability shows the spread of a data set around a point.
Example: Suppose, there exist 2 data sets with the same mean value:
A = 4, 4, 5, 6, 6Mean(A) = 5
B = 1, 1, 5, 9, 9Mean(B) = 5
So, to differentiate among the two data sets, R offers various measures of variability.
Following are some of the measures of variablity that R offers to differentiate between data sets:
Variance
Standard Deviation
Range
Mean Deviation
Interquartile Range
Variance is a measure that shows how far is each value from a particular point, preferably mean value. Mathematically, it is defined as the average of squared differences from the mean value.
Formula:
where,
 specifies variance of the data set specifies  value in data set specifies the mean of data setn specifies total number of observations
In the R language, there is a standard built-in function to calculate the variance of a data set.
Syntax: var(x)
Parameter:x: It is data vector
Example:
# Defining vectorx <- c(5, 5, 8, 12, 15, 16)  # Print variance of xprint(var(x))
Output:
[1] 23.76667

Standard deviation in statistics measures the spreaness of data values with respect to mean and mathematically, is calculated as square root of variance.
Formula:
where,
 specifies standard deviation of the data set specifies  value in data set specifies the mean of data setn specifies total number of observations
In R language, there is no standard built-in function to calculate the standard deviation of a data set. So, modifying the code to find the standard deviation of data set.
Example:
# Defining vectorx <- c(5, 5, 8, 12, 15, 16)  # Standard deviationd <- sqrt(var(x))  # Print standard deviation of xprint(d)
Output:
[1] 4.875107

Range is the difference between maximum and minimum value of a data set. In R language, max() and min() is used to find the same, unlike range() function that returns the minimum and maximum value of data set.
Example:
# Defining vectorx <- c(5, 5, 8, 12, 15, 16)  # range() function outputprint(range(x))  # Using max() and min() function# to calculate the range of data setprint(max(x)-min(x))
Output:
[1]  5 16
[1] 11

Mean deviation is a measure calculated by taking an average of the arithmetic mean of the absolute difference of each value from the central value. Central value can be mean, median, or mode.
Formula:
where,
 specifies  value in data set specifies the mean of data setn specifies total number of observations
In R language, there is no standard built-in function to calculate mean deviation. So, modifying the code to find mean deviation of the data set.
Example:
# Defining vectorx <- c(5, 5, 8, 12, 15, 16)  # Mean deviationmd <- sum(abs(x-mean(x)))/length(x)  # Print mean deviationprint(md)
Output:
[1] 4.166667

Interquartile Range is based on splitting a data set into parts called as quartiles. There are 3 quartile values (Q1, Q2, Q3) that divide the whole data set into 4 equal parts. Q2 specifies the median of the whole data set.
Mathematically, the interquartile range is depicted as:
IQR = Q3 – Q1
where,
Q3 specifies the median of n largest valuesQ1 specifies the median of n smallest values
In R language, there is built-in function to calculate the interquartile range of data set.
Syntax: IQR(x)
Parameter:x: It specifies the data set
Example:
# Defining vectorx <- c(5, 5, 8, 12, 15, 16)  # Print Interquartile rangeprint(IQR(x))
Output:
[1] 8.5

R-Statistics
R Language
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Change Color of Bars in Barchart using ggplot2 in R
Group by function in R using Dplyr
How to Change Axis Scales in R Plots?
How to Split Column Into Multiple Columns in R DataFrame?
Replace Specific Characters in String in R
How to filter R DataFrame by values in a column?
How to import an Excel File into R ?
Time Series Analysis in R
R - if statement
How to filter R dataframe by multiple conditions?