Respuesta :
The standard deviation of the data set is 7.60.
What is mean?
The mean is the mathematical average of a set of two or more numbers.
What is variance?
Variance is a measure of dispersion that takes into account the spread of all data points in a data set
What is standard deviation?
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.
According to the given question.
We have a data set: {31, 33, 36, 41, 34}
Now, the mean of the given data set is given by
[tex]M = \frac{31+33+36+41+34}{5} = \frac{141}{5} =28.2[/tex]
And, the variance of the given data set is given by
[tex]\sigma^{2} =\frac{(31-28.2)^{2} +(33-28.2)^{2} +(36-28.2)^{2} +(41-28.2)^{2} +(34-28.2)^{2}}{5}[/tex]
[tex]\implies \sigma^{2} = \frac{7.84+23.04+60.84+163.84+33.64}{5}[/tex]
[tex]\implies \sigma^{2} =\frac{289.2}{5} =57.84[/tex]
Therefore, the standard deviation of the given data set is give by
[tex]SD=\sqrt{\sigma^{2} }[/tex]
[tex]\implies SD = \sqrt{57.84} =7.60[/tex]
Hence, the standard deviation of the data set is 7.60.
Find out more information about mean, standard deviation and variance here:
https://brainly.com/question/12402189
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