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
2 answers:
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
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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.
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