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Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth. 20, 16, 18, 14, 9, 20, 16

PLEASE EXPLAIN STEP BY STEP HOW YOU FOUND THE STANDARD DEVIATION! Thank you! :)

2 Answers

1 vote

Plus them together and divide them by 7 give you the mean

mean = 16.1429

standard deviation = (20- mean)^2+ (16- mean)^2.......so on then divide by 7

Hope this helps :)

SD= 3.5628

User Patrickfdsouza
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3 votes

The mean is the sum divided by the number of numbers:

... mean = (20 +16 +18 + 14 +9 +20 +16)/7 = 113/7 = 16 1/7 = μ

The standard deviation can be computed several ways. My favorite is to compute the variance from the average of the squares. Again, that average is their sum divided by their number.

... average square = (400 +256 +324 +196 +81 +400 +256)/7 = 1913/7 = 273 2/7

Then the variance is the difference between the average square and the square of the average

.. variance = 273 2/7 - (16 1/7)² = 273 14/49 - 260 29/49 = 12 34/49

The standard deviation of the sample (s) is the square root of the variance: √(12 34/49) ≈ 3.563

Your numbers are

... μ ≈ 16.1, s ≈ 3.6

_____

The standard deviation here is that of this data set. If this data is a sample of a population, we often want the population standard deviation instead. To get that, multiply this value by √(n/n-1), where n is the sample size. Here, that is √(7/6) ≈ 1.08. (That gives you σ=3.8.)

In real life, the "step by step" is to enter the data into a suitable calculator and let it compute the statistics for you.

Please show your work to find the mean and standard deviation of the data. Round to-example-1
User Mel Pacheco
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