Respuesta :
The value of the standard deviation is 5.52.
According to the statement
we have to find the value of the standard deviation of the given data.
For this purpose, we know that the
The standard deviation is the average amount of variability in your dataset.
From given information, the data set is:
(19, 10, 5, 6)
Firstly we find the mean value, so,
Mean value = sum of data values / number of data values.
Mean value = 19+10+5+6/4
Mean value = 40/4
Mean value = 10.
Now, the standard deviation formula is:
[tex]Standard deviation = \sqrt\frac{{(x - mean)^{2}}}{n}[/tex]
[tex]Standard deviation = \sqrt\frac{{(19 -10)^{2} + (10-10)^{2} +(5-10)^2 +(6-10)^{2} }}{4}[/tex]
Then solve it
[tex]Standard deviation = \sqrt\frac{{81 +0 +25 +16 }}{4}[/tex]
[tex]Standard deviation = \sqrt\frac{{122}}{4}[/tex]
[tex]Standard deviation = \sqrt {30.5[/tex]
Now the sd value become
standard deviation = 5.52
So, The value of the standard deviation is 5.52.
Learn more about standard deviation here
https://brainly.com/question/475676
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