Answer:
Mean = 8
Mode = 12
Median = 7.5
Standard deviation = 3.07
Step-by-step explanation:
We are given the following sample in the question:
6, 12, 7, 8, 4, 5, 12, 10
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{64}{8} = 8[/tex]
Sum of squares of differences = 66
[tex]S.D = \sqrt{\dfrac{66}{7}} = 3.07[/tex]
Mode is the most frequent observation of data.
Mode = 12
Since it repeats two times.
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Sorted data: 4, 5, 6, 7, 8, 10, 12, 12
[tex]\text{Median} = \dfrac{4^{th}+5^{th}}{2} = \dfrac{7+8}{2}=7.5[/tex]
