Page 129 - Data Science class 10
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Step 3 Calculate the square of each of the differences.
We get:
–0.5 × –0.5 = 0.25
1.5 × 1.5 = 2.25
–2.5 × -2.5 = 6.25
1.5 × 1.5 = 2.25
Step 4 Find the average of squared numbers.
11
0.25 + 2.25 + 6.25 + 2.25 =
4
= 2.75
Step 5 Finally, find the square root of the variance. Which results in a standard deviation measure of approximately
1.65. The whole calculation is shown in the table given below:
Data Point Mean Distance from mean Square of distances
5 5.5 -0.5 0.25
7 5.5 1.5 2.25
3 5.5 -2.5 6.25
7 5.5 1.5 2.25
Mean = sum/n 5.5
Sum of squares 11.00
Variance = sum of squares/N 2.75
Standard Deviation = Square root of the Variance 1.65
The standard deviation 1.65 can be represented graphically as given below:
Standard deviation curve
0.25
0.2
0.15
0.1
0.05
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
A few real-life applications of standard deviation include:
• Grading Tests: If teacher wishes to know whether students are performing at the same level or whether there
is a higher standard deviation.
• Calculate the Results of Any Survey: If someone wants to have some measure of the reliability of the responses
received in the survey, they can predict how a larger group of people may answer the same questions.
Use of Statistics in Data Science 127

