How to Calculate Standard Deviation (With Example) – A Must-Know Skill in Every Data Analyst Course

In the era of data analysis courses, one of the most important conception every seeking analyst must know is Standard Deviation. Either you’re doing a free data analyst course or a specialized course in data analyst, knowing how to calculate and interpret standard deviation is vital.

At Statistics Solutions, we offer both free data analytics courses and specialized data analyst classes that impart notions like standard deviation in the easiest, most practical way—especially using tools like IBM SPSS and SPSS software.

What is Standard Deviation?

Standard deviation is also called the root mean square deviation. It shows dispersion of data points from the mean. In simple terms, it shows variability of a data.

Formula for Standard Deviation

Where:

x_i= Value of individual observation

µ = Mean of observations

N= Number of observations

This formula is explained in our data analysis free course and demonstrated using ibmspss tools.

Step-by-Step: Standard Deviation Example

• Steps to calculate Standard Deviation:
  
  • Calculate mean (x̄) of all values (x).
  • Find deviation of each from mean, that is, (x-x̄)
  • Find sqaure of (x-x) i.e. (x-x̄)².
  • Find the sum of all squares [Ʃ(x-x̄)²].
  • Divide sum by number of participants and take square root to get  standard deviation

Standard Deviation = [(Ʃ(x-x̄)²)/n]

• Example 1:   Let’s calculate the Standard Deviation of height of 6 participants from the following data:

Table 3.13: Data for Example 1

S. No.	Height (cm) (x)
1	120.1
2	122.8
3	135
4	150.6
5	155.2
6	128.3
	Mean (x̄)  = 135.3

To calculate standard deviation, first step is to calculate mean. Mean of the above data came out to be 135.3. Now the next step is to calculate deviation of mean from each value. For this, mean will be subtracted from each value, as follows:

S. No.	Height (cm) (x)	Deviation from mean (x- x̄)
1	120.1	120.1-135.3 = -15.2
2	122.8	122.8-135.3 = -12.5
3	135	135-135.3 = -0.3
4	150.6	150.6-135.3 = 15.3
5	155.2	155.2-135.3 = 19.9
6	128.3	128.3-135.3 = -7
	Mean (x̄)  = 135.3

Once all deviations are calculated, amongst which some values are negative, we need to square all deviations [(x- x̄)²], as follows:

S. No.	Height (cm) (x)	Deviation from mean (x- x̄)	Square of deviation (x- x̄)2
1	120.1	120.1-135.3 = -15.2	(15.2)2 =231.4
2	122.8	122.8-135.3 = -12.5	(12.5)2 = 156.25
3	135	135-135.3 = -0.3	(0.3)2 = 0 .09
4	150.6	150.6-135.3 = 15.3	(15.3)2 = 234.09
5	155.2	155.2-135.3 = 19.9	(19.9)2 = 396.01
6	128.3	128.3-135.3 = -7	(7)2 =49
	Mean (x̄)  = 135.3

After calculating square of deviation for each observation, last step is to calculate standard deviation. Standard deviation is calculated by calculating mean of all square of deviations (Add up all absolute deviations and divide by number of observations) and taking a square root of that mean, as follows:

S. No.	Height (cm) (x)	Deviation from mean (x- x̄)	Square of deviation (x- x̄)2	Standard Deviation √ Ʃ (x- x̄)2/n
1	120.1	120.1-135.3 = -15.2	(15.2)2 =231.4	√(231.4+156.25 +0.09+234.09+396.01+49)/6 = √1066.84/6 = √177.81 = 13.3
2	122.8	122.8-135.3 = -12.5	(12.5)2 = 156.25
3	135	135-135.3 = -0.3	(0.3)2 = 0 .09
4	150.6	150.6-135.3 = 15.3	(15.3)2 = 234.09
5	155.2	155.2-135.3 = 19.9	(19.9)2 = 396.01
6	128.3	128.3-135.3 = -7	(7)2 =49
	Mean (x̄)  = 135.3

So 13.3 is the standard deviation in above example.

We walk you through this process with real-life datasets in our data analyst classes, using SPSS soft ware for quicker computation and better visualization.

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