We are given the following data
5 8 10 4 8 10 3 8
Mean:
The mean of the data is given by
[tex]mean=\frac{\sum x_i}{n}[/tex]Where xi are the individual values and n is the number of values in the data set.
[tex]mean=\frac{5+8+10+4+8+10+3+8}{8}=\frac{56}{8}=7[/tex]So, the mean of the data set is 7.
Median:
First, we need to arrange the data in ascending order (least to greatest)
3, 4, 5, 8, 8, 8, 10, 10
The median value is given by
[tex]median=\frac{(n+1)}{2}=\frac{8+1}{2}=\frac{9}{2}=4.5^{th}\;value[/tex]This means that the median is between the 4th and 5th value.
The 4th and 5th both values are 8.
[tex]median=\frac{8+8}{2}=\frac{16}{2}=8[/tex]Therefore, the median of the data set is 8
Mode:
The mode is the most repeated value in the data set.
As you can see, the value 8 is most repeated (3 times)
Therefore, the mode of the data set is 8
Standard deviation:
The standard deviation is given by
[tex]SD=\sqrt{\frac{\sum(x_i-\bar{x})}{n-1}}[/tex]Where x_bar is the mean, and n is the number of values in the data set.
[tex]\begin{gathered} SD=\sqrt{\frac{(5-7)^2+(8-7)^2+(10-7)^2+(4-7)^2+(8-7)^2+(10-7)^2+(3-7)^2+(8-7)^2}{8-1}} \\ SD=2.67 \end{gathered}[/tex]The standard deviation of the data set is 2.67
Summary:
Mean = 7
Median = 8
Mode = 8
Standard deviation = 2.67