- So what is the standard deviation?
- Importance on Standard deviation
- Find the Standard deviation in R for values in a list
- Finding the Standard deviation of the values stored in a CSV file
- High and Low Standard Deviation
- Example #1: Standard Deviation for a List of Even Numbers
- Example #2: Standard Deviation for US Population Data
- Conclusion

- CONTENTS

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Being a statistical language, R offers standard function sd(’ ') to find the standard deviation of the values.

**‘Standard deviation is the measure of the dispersion of the values’.**- The higher the standard deviation, the wider the spread of values.
- The lower the standard deviation, the narrower the spread of values.
- In simple words the formula is defined as -
**Standard deviation is the square root of the ‘variance’.**

Standard deviation is very popular in the statistics, but why? the reasons for its popularity and its importance are listed below.

- Standard deviation converts the negative number to a positive number by
**squaring**it. - It shows the
**larger deviations**so that you can particularly look over them. - It shows the
**central tendency,**which is a very useful function in the analysis. - It has a major role to play in
**finance, business, analysis, and measurements.**

Before we roll into the topic, keep this definition in your mind!

**Variance** - It is defined as the squared differences between the observed value and expected value.

In this method, we will create a list ‘x’ and add some value to it. Then we can find the standard deviation of those values in the list.

```
x <- c(34,56,87,65,34,56,89) #creates list 'x' with some values in it.
sd(x) #calculates the standard deviation of the values in the list 'x'
```

**Output —> 22.28175**

Now we can try to extract specific values from the list ‘y’ to find the standard deviation.

```
y <- c(34,65,78,96,56,78,54,57,89) #creates a list 'y' having some values
data1 <- y[1:5] #extract specific values using its Index
sd(data1) #calculates the standard deviation for Indexed or extracted values from the list.
```

**Output —> 23.28519**

In this method, we are importing a CSV file to find the standard deviation in R for the values which are stored in that file.

```
readfile <- read.csv('testdata1.csv') #reading a csv file
data2 <- readfile$Values #getting values stored in the header 'Values'
sd(data2) #calculates the standard deviation
```

**Output —> 17.88624**

In general, The values will be so close to the average value in **low standard deviation** and the values will be far spread from the average value in the **high standard deviation.**

We can illustrate this with an example.

```
x <- c(79,82,84,96,98)
mean(x)
---> 82.22222
sd(x)
---> 10.58038
```

To plot these values in a bar graph using in R, run the below code.

To install the ggplot2 package, run this code in R studio.

**-–> install.packages(“ggplot2”)**

```
library(ggplot2)
values <- data.frame(marks=c(79,82,84,96,98), students=c(0,1,2,3,4,))
head(values) #displayes the values
marks students
1 79 0
2 82 1
3 84 2
4 96 3
5 98 4
x <- ggplot(values, aes(x=marks, y=students))+geom_bar(stat='identity')
x #displays the plot
```

In the above results, you can observe that most of the data is clustering around the mean value(79,82,84) which shows that it is a **low standard deviation**.

Illustration for **high standard deviation**.

```
y <- c(23,27,30,35,55,76,79,82,84,94,96)
mean(y)
---> 61.90909
sd(y)
---> 28.45507
```

To plot these values using a bar graph in ggplot in R, run the below code.

```
library(ggplot2)
values <- data.frame(marks=c(23,27,30,35,55,76,79,82,84,94,96), students=c(0,1,2,3,4,5,6,7,8,9,10))
head(values) #displayes the values
marks students
1 23 0
2 27 1
3 30 2
4 35 3
5 55 4
6 76 5
x <- ggplot(values, aes(x=marks, y=students))+geom_bar(stat='identity')
x #displays the plot
```

In the above results, you can see the widespread data. You can see the least score of 23 which is very far from the average score 61. This is called the **high standard deviation**

By now, you got a fair understanding of using the sd(’ ') function to calculate the standard deviation in the R language. Let’s sum up this tutorial by solving simple problems.

Find the standard deviation of the even numbers between 1-20 (exclude 1 and 20).

**Solution:** The even numbers between 1 to 20 are,

-–> 2, 4, 6, 8, 10, 12, 14, 16, 18

Lets find the standard deviation of these values.

```
x <- c(2,4,6,8,10,12,14,16,18) #list of even numbers from 1 to 20
sd(x) #calculates the standard deviation of these
values in the list of even numbers from 1 to 20
```

**Output —> 5.477226**

Find the standard deviation of the state-wise population in the USA.

For this, import the CSV file and read the values to find the standard deviation and plot the result in a histogram in R.

```
df<-read.csv("population.csv") #reads csv file
data<-df$X2018.Population #extarcts the data from population
column
mean(data) #calculates the mean
View(df) #displays the data
sd(data) #calculates the standard deviation
```

**Output** ----> **mean** = 6432008, **Sd** = 7376752

Finding the standard deviation of the values in R is easy. R offers standard function sd(’ ') to find the standard deviation. You can create a list of values or import a CSV file to find the standard deviation.

**Important:** Don’t forget to calculate the standard deviation by extracting some values from a file or a list through indexing as shown above.

Use the comment box to post any kind of doubts regarding the sd(’ ') function in R. Happy learning!!!

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hey! this was help full but how to find sd for a grouped frequency data distribution for eg a table like this x f 5-10 12 10-20 28 20-30 65 30-40 121 40-50 175 50-60 198 60-70 176 70-80 120 80-90 66 90-100 27 100-115 9 115-120 3 … what to do after making them into a data.frame()

- Saptharishee M