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How many standard deviations away from the mean is the median.

The mean and the median are central tendency measures in statistics. One of the measurements of dispersion is the standard deviation, which is used to show how much individuals in a group differ from the mean. The Z-score indicates how far a value is above or below the mean in terms of standard deviation. The z-score is calculated using the following formula:

$z=\frac{x-渭}{蟽}$

$$\begin{gathered} x=isanydatavalue \\ 渭=isthepopulationmean \\ 蟽=isthepopulations\tan darddeviation \end{gathered}$$

In the given example, we are given the below parameters about the population:

$$\begin{gathered} 渭=1000\mathrm{FTES} \\ median=1014FTES \\ 蟽=474FTES \\ firstquartile=528.5\mathrm{FTES} \\ thirdquartile=1447.5FTES \\ n=29years \end{gathered}$$

The z-score formula is now used to determine how many standard deviations distant from the mean the median is.

$$\begin{gathered} z=\frac{\text{Median}-渭}{蟽} \\ =\frac{1014-1000}{474} \\ z=0.03 \end{gathered}$$

Hence the median is 0.03 standard deviations above the mean.