Download Standard Deviation Variance Example

Standard Deviation Notes
Name: ________________________
Read p.609 in the textbook.
Deviation just means how far from the normal
Standard Deviation
The standard deviation measures the spread of the data about the mean value. It is
useful in comparing sets of data which may have the same mean but a different range. For
example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30.
However, the second is clearly more spread out. If a set has a low standard deviation, the
values are not spread out too much.
Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance. So now, "What is the Variance?"
Variance
The Variance is defined as: The average of the squared differences from the Mean.
To calculate the variance follow these steps:



Work out the Mean (the simple average of the numbers)
Then for each number: subtract the Mean and square the result (the squared difference).
Then work out the average of those squared differences.
Example
You and your friends have just measured the heights of your dogs (in millimeters):
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.
Find out the Mean, the Variance, and the Standard Deviation.
Your first step is to find the Mean:
Answer: Mean =
600 + 470 + 170 + 430 + 300
5
=
1970
5
= 394
so the mean (average) height is 394 mm.
To calculate the Variance, take each difference, square it, and then average the result:
600 – 394 =
470 – 394 =
170 – 394 =
430 – 394 =
300 – 394 =
So, the Variance is 21,704. And the Standard Deviation is just the square root of Variance, so:
Standard Deviation: σ =
21,704 = 147.32... = 147 (to the nearest mm)
So, using the Standard Deviation we have a "standard" way of knowing what is normal, and what
is extra large or extra small. Rottweilers are tall dogs. And Dachshunds are a bit short ... but
don't tell them!
Examples:
1) Ten friends scored the following marks in their end-of-year math exam: 23%, 37%,
45%, 49%, 56%, 63%, 63%, 70%, 72% and 82%. What was the standard deviation of their
marks?
2) What is the standard deviation for the numbers: 75, 83, 96, 100, 121 and 125?