The standard deviation of the data is 18 .1
How to calculate the standard deviation
Use the formula:
SD = √∑(x - ₓ⁻)^2 ÷ n
Where
x = data
x bar = mean
n = number of data set
To find the mean,
Use the formula:
mean = sum of data set ÷ number of data set
mean = 8 + 12+ 14+ 8+ 9 + 5 + 17 + 19+ 31+ 8 ÷ 10
Mean = 131÷ 10 = 13. 1
Standard deviation = [tex]\sqrt\frac{(8 -13.1) + (12-13.1) + (14-13.1) + (8-13.1) + (9- 13.1) + (5-13.1) + (17-13.1) + (19-13.1) + (31-13.1) + (8-13.1)}{10}[/tex]
Standard deviation = [tex]\frac{(-5.1 ) + (-1-.1) + (1.1) + (-5.1) + (-4.1) + (-8.1) + (3.9) + (5. 9) + (17.9) + 95.1)}{10}[/tex]
Standard deviation = [tex]\sqrt{\frac{57.4^{2} }{10} }[/tex]
Standard deviation = [tex]\sqrt{\frac{3294. 76}{10} }[/tex]
Standard deviation = [tex]\sqrt{329. 476}[/tex]
Standard deviation = 18. 15
Therefore, the standard deviation is 18. 1
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