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Understanding Standard Deviation in Data Analysis

Learn how to calculate, interpret, and apply standard deviation in statistical analysis. Understand the spread of data points around the mean using examples for clarity.

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Understanding Standard Deviation in Data Analysis

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  1. Standard Deviation

  2. The Standard Deviation is a number that measures how far away each number in a set of data is from their mean.

  3. If the Standard Deviation is large, it means the numbers are spread out from their mean.If the Standard Deviation is small, it means the numbers are close to their mean. large, small,

  4. Here are the scores on the math quiz for Team A: Average: 81.5

  5. The Standard Deviation measures how far away each number in a set of data is from their mean. For example, start with the lowest score, 72. How far away is 72 from the mean of 81.5? 72 - 81.5 = - 9.5 - 9.5

  6. Or, start with the lowest score, 89. How far away is 89 from the mean of 81.5? 89 - 81.5 = 7.5 - 9.5 7.5

  7. Distance from Mean So, the first step to finding the Standard Deviation is to find all the distances from the mean.

  8. Distance from Mean So, the first step to finding the Standard Deviation is to find all the distances from the mean.

  9. Distance from Mean Distances Squared Next, you need to square each of the distances to turn them all into positive numbers

  10. Distance from Mean Distances Squared Next, you need to square each of the distances to turn them all into positive numbers

  11. Distance from Mean Distances Squared Add up all of the distances Sum: 214.5

  12. Distance from Mean Distances Squared Divide by (n) where n represents the amount of numbers you have. Sum: 214.5 (10) = 21.45

  13. Distance from Mean Distances Squared Finally, take the Square Root of the average distance Sum: 214.5 (10) = 21.45 = 4.63

  14. Distance from Mean Distances Squared This is the Standard Deviation Sum: 214.5 (10) = 21.45 = 4.63

  15. Distance from Mean Distances Squared Now find the Standard Deviation for the other class grades Sum: 2280.5 (10) = 228.05 = 15.10

  16. Now, lets compare the two classes again 81.5 81.5 4.63 15.01

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