Standard Deviation in R

Overview Of Standard Deviation in R

Standard deviation in R is a statistic that measures the amount of dispersion or variation of a set of value, generally, it is used when we are dealing with values where we have to find the difference between the values and the mean.

Mathematical formula of standard deviation:

Where,

• S: Sample standard deviation.
• N: Number of observations.
• xi: Observed value of the sample item.
• x̅: Mean value of the observation.

How to Calculate Standard Deviation?

Steps to calculate Standard deviation are:

• Step 1: Calculate the mean of all the observations.
• Step 2: Then for each observation, subtract the mean and double the value of it (Square it).
• Step 3: We got some values after deducting mean from the observation, do the summation of all of them.
• Step 4: Lastly, divide the summation with the number of observations minus 1.

You will get the standard deviation as a result after completing 4 steps.

Examples with Steps of Standard Deviation

Let’s take an example and follow these steps.

Example #1

Data set looks like,

4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2

Step 1: Calculate the mean of all the observations,

• Mean = (4 + 8 + 9 + 4 + 7 + 5 + 2 + 3 + 6 + 8 + 1 + 8 + 2 + 6 + 9 + 4 + 7 + 4 + 8 + 2) / 20
• Mean = 107/20
• Mean = 5.35

Step 2: For each observation, subtract the mean, we will put it in the tabular form for the convenience,

Double the value of the column second (Observation – Mean)^2.

Step 3: Summation of all the values present in the above column.

1.8225 + 7.0225 + 13.3225 + 1.8225 + 2.7225 + 0.1225 + 11.2225 + 5.5225 + 0.4225 + 7.0225 + 18.9225 + 7.0225 + 11.2225 + 0.4225+13.3225 + 1.8225 + 2.7225 + 1.8225 + 7.0225 + 11.2225 = 126.55

Step 4: We will calculate the Standard deviation, by dividing summation with the number of observations minus 1 and we will square root the result.

Standard Deviation = (126.55/19)^0.5 = 2.58079

Example #2

Now we will look into some other examples with different datasets. In this example, we have two columns. In one column there are some alphabetic codes which we assigned to the people and in the next column, we have the age of those sets of people.

Step 1: We will upload the excel file in R. Here we will use read.csv function because our excel file is in csv format. Suppose this table is in excel, so how this will work in Rstudio, we will discuss this step by step. The name of the excel file is “alphabetic code”.

The function for the same looks like,

SD_age = read.csv("alphabetic code.csv")

Step 2: calculating the standard deviation from the excel file. As we can see, that 2 column contains a numeric value. We will run our code on that column specifically,

In R, the syntax for Standard Deviation looks like this:

standard_deviation_age = sd(SD_age)
standard_deviation_age

The output of the codes provides us the Standard deviation of the dataset. The standard deviation of the Age is 15.52926.

Methods of Standard Deviation in R

There are multiple methods to calculate Standard deviation in R. We will here discuss one long method and one very short method.

1. Long Method

This method will incorporate the same steps which we did earlier in this article, the only difference now is we will use R commands.

Step 1: Calculate the mean of all the observations.

Code:

dataset = c(4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2)
meandataset = mean(dataset)
meandataset

Output:

Step 2: For each observation, subtract the mean from all the observations of the dataset. For this, we will make a function in R, which will help us to find [Observation-Mean].

Code:

dataset = c(4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2)
meandataset = mean(dataset)
sumdataset = function(dataset){dataset-meandataset}
Observation_Mean = sumdataset(dataset)
Observation_Mean

Output:

The output shows Observation – Mean for all the values in our dataset. Now we will square each value of this output an do the summation.

Code:

dataset = c(4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2)>
meandataset = mean(dataset)>
sumdataset = function(dataset){dataset-meandataset}
Observation_Mean = sumdataset(dataset)
square_Observation_Mean = Observation_Mean*Observation_Mean
square_Observation_Mean

Output:

Step 3: Summation of all the values present in the above column. Now we will add all these [(Observation – Mean)^2].

Code:

dataset = c(4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2)
meandataset = mean(dataset)
sumdataset = function(dataset){dataset-meandataset}
Observation_Mean = sumdataset(dataset)
square_Observation_Mean = Observation_Mean*Observation_Mean
sum_square_Observation_Mean = sum(square_Observation_Mean)
sum_square_Observation_Mean

Output:

Step 4: We will calculate the Standard deviation. No, we will put all the necessary information which we derive in all the above steps into this function:

• Standard Deviation = (126.55/19)^0.5
• Standard Deviation = 2.58079

In R, the syntax for Standard Deviation looks like this:

Code:

dataset = c(4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2)
meandataset = mean(dataset)
sumdataset = function(dataset){dataset-meandataset}
Observation_Mean = sumdataset(dataset)
square_Observation_Mean = Observation_Mean*Observation_Mean
sum_square_Observation_Mean = sum(square_Observation_Mean)
standard_deviation = sqrt(sum_square_Observation_Mean/19)
standard_deviation

Output:

Hence we can see the Standard deviation is the same which we got earlier.

2. Short Method

Syntax in R for the direct method looks like,

sd(x, na.rm = FALSE)

Where sd is Standard deviation. x is those set values for which we need to find the standard deviation. na.rm, if it is true then it will remove all the missing value from the dataset/ matrix /data frames etc. And if it is false, then it won’t remove missing value from the data set.

Code:

dataset = c(4,8,9,4,7,5,2,3,6,8,1,8,2,6,9,4,7,4,8,2)
sd(dataset)

Output:

Conclusion

Standard deviation tells us how much our observations in the datasets are spread out from the actual mean. Significance of low and high standard deviation is:

• High Standard deviation tells us that the numbers/observations in the dataset are more spread out.
• Low Standard deviation tells us that the numbers/observations in the dataset are less spread out or we can say that they are close to mean.

Recommended Articles

This is a guide to Standard Deviation in R. Here we discuss the steps and methods of Standard Deviation in R along with examples and code implementation. You may also have a look at the following articles to learn more –

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