Cameron Russell

2022-01-27

The numbers of television licenses brought at a particular post office on a sample of 5 randomly chosen weekdays were 15, 9, 23, 12, and 17. How do you find the mean and the standard deviation?

immablondevl

Expert

Explanation:
To find the mean for any given set of numbers, you add all of the numbers together, and divide that sum by how many numbers there were. For example, if you have the numbers 15,9,23,12 and 17, to find the mean you would first add them together (15+9+23+12+17=76), then you would divide their sum by how many numbers were used ($\frac{76}{5}=15.2$), and there you have your mean.
To find the deviation is more complicated, but still doable. There are 4 steps to find the standard deviation:
1. Work out the Mean (which we have done)
2. Then for each number: subtract the Mean and square the result
3. Then work out the mean of those squared differences.
4. Take the square root of that and we are done!
Step 1 is completed, and step 2 goes like this: (15-15.2=-0.2)(9-15.2=-6.2)(23-15.2=7.8)(12-15.2=-3.2) and (17-15.2=1.8).
Step 2 continued, we now square these answers to get
$\left(-{6.2}^{2}=38.44\right),\left(-{0.2}^{2}=0.04\right),\left({7.8}^{2}=60.84\right),\left(-{3.2}^{2}=10.24\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\left({1.8}^{2}=3.24\right)$
Now for step 3, where we add all the new answers together and then divide them by how many new answers there were, so (60.84+10.24+3.24+38.44+0.04=112.8), then $\frac{112.8}{5}=22.56$
Finally, for step 4 we take the square root of the answer to find the standard deviation, which is $\sqrt{22.56}\approx 4.75$.

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