What does standard deviation of a set of data tell you?
2 answers:
Answer:
It tells us about how our set of data is spread out as compared to our mean or expected value.
Explanation:
Note: Standard deviation is represented by Greek Letter sigma.
For example: A teacher in a class of particular students takes a learning ability test from the students. Average or mean marks of students is 52 with +/- 10 marks. Then 1σ (Sigma = standard deviation) it means 1 standard deviation = 68% students will lie in between 52 + 10 =62 marks and 52-10 = 42 marks region.
2σ (2 standard deviation) means among the students 95% of them will lie between 52 + 20 =72 and
52-20= 32 marks region.
3σ (3 standard deviation) means 99.7% of the students will lie in the region where 52 + 30 = 82 and 52 – 30 = 22 marks region.
So for 3σ (3 Standard Deviations), only 0.3% of the total students deviate +/-30 marks from the average. It means 0.15% students will have marks less than 22 and 0.15% students will have marks greater than 82.
In the schematic attached, I have tried to make you understand through a diagram. Please refer to the schematic 1.
It tells us about the how our set of data is spread out as compared to our average or mean. And distance from mean can be calculated through number of standard deviations that the data is how much below or above the average.
For example:
For 1σ 68% students will come under the curve of “Average Learners” and rest of 32% will come under the curve of “Poor Learners” and “Very Talented Learners”.
For 2σ 95% of the students will come under the curve of “Average Learners” and rest will come under the curve of “Poor Learners” and “Very Talented Learners”.
For 3σ 99.7% of the students will come under the curve of “Average Learners” and rest of 0.3% will come under the curve of “Poor Learners” and “Very Talented Learners”.
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