Standard Deviation
By DarthVader
Date: 2022-07-10
Topic: 145 see comments
Post views: 1038
Standard Deviation
The spread of a dataset can be calculated by taking the ‘range’ of the data, but a more accurate way to calculate the spread of the dataset, is to calculate the standard deviation.
- The standard deviation is an accurate and reliable way to measure the spread of a dataset.
- Engineers use standard deviation to calculate the spread of data more reliably.
Steps for finding the standard deviation of a dataset
- Find the mean of the dataset
- Find the difference of each value from the mean - these are the ‘deviations’, often labelled as ‘d’ values
- Square each deviation - this gives the ‘d2’ values
- Find the mean of these squared deviations - this number is the ‘mean squared deviation’, better known as the variance. If your data represent a sample of a potentially larger dataset, find the mean by dividing by ‘n - 1’, where ‘n’ is the number of data points
- Find the square root of the variance to get the ‘root mean squared deviation'; that is, the standard deviation
Standard deviation is often represented by ‘SD’ or ‘σ’
Normal distribution
A graph of a dataset that has a normal distribution produces a symmetrical bell-shaped curve.
For data that is normally distributed:
- 68.26% of the values lie within 1 standard deviation of the mean
- 95% of the values lie within 1.96 standard deviations of the mean
- 95.44% of the values lie within 2 standard deviations of the mean
- 99.73% of the values lie within 3 standard deviations of the mean
Hints:
- If the standard deviation of a dataset is 0.5, and the mean of the dataset is 20, you could say that 99.73% of the data points will lie within 3 standard deviations (3 × 0.5) of the mean (20). In this case that would be:
3 × 0.5 = 1.5
20 + 1.5 = 21.5
20 − 1.5 = 18.5
So in this case, 99.73% of the values lie between 18.5 and 21.5.
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