The concepts of mathematics are very integral. They are used in almost all fields and help people in day-to-day lives also. Many concepts like Algebra, Venn diagrams, Geometry, Standard deviation, etc are widely used. They must be well understood from the beginning only.
Standard deviation is one important concept in mathematics. It is used to find out the deviation in a given data set. It values the spread in the data set.
- It’s simple to understand how to calculate standard deviation
SD = ∑|x- µ |^2N
- Real-life implications of Standard deviation-
- It is used in the evaluation of the result of students in a class. Their marks can be compared to the class average and their deviation can be observed to analyze which students need more attention and which student is doing good.
- Standard deviation helps in analyzing the weather deviation. The two data sets can be compared to accurately predict the weather conditions of the future.
- Standard deviation is also used in quality control. The standard quality is set and then the quality of the products so made is evaluated. The product whose quality deviates by huge margins from the standard is eliminated. This way consistency in the overall production process is maintained.
- Employees can benefit from it too. In an organization, they can compare the deviation between their salary and the average salary of the organization to decide if they are fairly paid or not.
- The calculation of standard deviation can be understood step by step-
The data set given is 6, 2, 3, 1
. Step 1-
The first step will be finding the mean of all the values in the data set.
Here, the calculation will be-
Mean/µ = (6 + 2 + 3 + 1) / 4 = 12 / 4 = 3
Thus, the mean of the values is 3
. Step 2-
In this step, the difference between all the values in the data set and the mean will be found and the result will be subsequently squared. In other words, the distance between the data value and the mean will be found to see how far they are.
| x – µ |^ 2 will be found in this case.
The calculation here will be-
6 – 3 = 3
3^2 = 9
2 – 3 = -1
-1^2 = 1
3 – 3 = 0
0^2 = 0
1 – 3 = -2
-2^2 = 4
. Step 3-
In this step, the values obtained by subtracting the values in the data set and the mean and squaring them will be added.
∑ | x – µ |^2 will be found in this step.
Here, the calculation will be-
9 + 1 + 0 + 4 = 14
- Step 4-
In this step, the final value obtained in the previous step will be divided by the number of values in the data set, which here is 4.
Thus, the calculation will be 14 / 4 = 3.5
- Step 5 –
In this step, the final value will be received. To find that, the square root of the value found in step 4 will be done.
3.5 = 1.87
By following 5 simple steps the final result can be achieved easily and simply.
Standard deviation is used widely in statistics. It is used for research, data analysis, etc. its calculation however may seem complex at first but with gradual practice, one can master it and play with different data sets. It is a very important concept in mathematics. Students should be well taught about it in the beginning. There are many good coaching centers and math websites like Cuemath where students can be taught concepts with clarity and the practice questions available there can help them in practicing them well. It is very important while calculating standard deviation that calculations should be properly checked at each stage because they are to be further used in steps. One wrong calculation will be troublesome and one will need to do everything from scratch.