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Question
measures of variability
some text about a dataset, then data values like 26, 28, 21, 22, 30, 25, 22, 29, 23, 22, 26, 32, 28, 30, 25, 21, 24, 27, 31, 29 (maybe?); then boxes with 0 per inning, 23.53 percents, 5.03 percents, 1.03 percents
Step1: Calculate the mean
First, find the average of the data set.
$\text{Mean} = \frac{26 + 24 + 21 + 27 + 20 + 25 + 32}{7} = \frac{175}{7} = 25$
Step2: Find squared differences
Subtract the mean from each value, square the result.
$(26-25)^2=1$, $(24-25)^2=1$, $(21-25)^2=16$, $(27-25)^2=4$, $(20-25)^2=25$, $(25-25)^2=0$, $(32-25)^2=49$
Step3: Calculate variance
Find the average of the squared differences (sample variance, divide by $n-1$).
$\text{Variance} = \frac{1+1+16+4+25+0+49}{7-1} = \frac{96}{6} = 16$
Step4: Compute standard deviation
Take the square root of the variance.
$\text{Standard Deviation} = \sqrt{16} = 4$
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