Answer :
Final answer:
The standard deviation measures how spread out numbers are from their mean in Mathematics. It is calculated by finding the mean of the data set, subtracting the mean from each number and squaring the result, then finding the mean of these squared differences to obtain the variance, and finally, the standard deviation is the square root of the variance.
Explanation:
The question asks for the Standard Deviation for the given data set. This is a measure of how spread out numbers are in statistics and is utilized within the field of Mathematics. The first step in calculating this is to find the mean of your data set. Then subtract the mean from each number and square the result. Find the mean of these squared differences and this gives you the Variance. The Standard Deviation is then found by taking the square root of the Variance.
For your data set: 34.1, 22.4, 55, 47.1, 39.8, 28.6, 44, 27.1, 35.9, 40.2 it proceeds as follows:
- Find the mean (average) of your data set: (34.1+22.4+55+47.1+39.8+28.6+44+27.1+35.9+40.2)/10 = 37.42
- Subtract the Mean from each number in your data set and square the result: [(34.1-37.42)², (22.4-37.42)²,...]
- Then calculate the mean of these squared differences to get the Variance
- Lastly, the Standard Deviation is the square root of the Variance.
In practice, you can use a calculator or computer software to perform these computations more efficiently.
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