# What are the mean, median, mode, variance and standard deviation of {4,6,7,5,9,4,3,4}?

Nov 23, 2015

Mean $= 5.25 \textcolor{w h i t e}{\text{XXX}}$Median $= 4.5 \textcolor{w h i t e}{\text{XXX}}$Mode $= 4$
Population: Variance $= 3.44 \textcolor{w h i t e}{\text{XXX}}$Standard Deviation $= 1.85$
Sample: $\textcolor{w h i t e}{\text{X}}$Variance $= 43.93 \textcolor{w h i t e}{\text{XXX}}$Standard Deviation $= 1.98$

#### Explanation:

Mean is the arithmetic average of the data values

Median is the middle value when the data values have been sorted (or the average of the 2 middle values if there are an even number of data values).

Mode is the data value(s) the occur with the greatest frequency.

Variance and Standard Deviation depend upon whether the data is assumed to be the entire population or only a sample from the entire population.

Population Variance $\left(\textcolor{b l a c k}{{\sigma}_{\text{pop}}^{2}}\right)$
is the sum of the squares of the differences between each data value and the mean, divided by the number of data values.

Population Standard Deviation $\left(\textcolor{b l a c k}{{\sigma}_{\text{pop}}}\right)$
is the square root of ${\sigma}_{\text{pop}}^{2}$

Sample Variance $\left(\textcolor{b l a c k}{{\sigma}_{\text{smpl}}^{2}}\right)$
is the sum of the squares of the differences between each data value and the mean, divided by one less than the number of data values.

Sample Standard Deviation$\left(\textcolor{b l a c k}{{\sigma}_{\text{smpl}}}\right)$
is the square root of ${\sigma}_{\text{smpl}}^{2}$