Descriptive Statistics

Median

Find the median of a data set by sorting the values and selecting the middle element (odd count) or averaging the two middle elements (even count).

Example

Sort the data and choose the middle value.

highlighted = computed this step

Step 1 — Data

List the data values.

posx1327324955\begin{array}{cc}\text{pos} & \text{x} \\ 1 & 3 \\ 2 & 7 \\ 3 & 2 \\ 4 & 9 \\ 5 & 5\end{array}

Step 2 — Sort

Sort the data from least to greatest.

posx1223354759\begin{array}{cc}\text{pos} & \text{x} \\ 1 & \hlmath{2} \\ 2 & \hlmath{3} \\ 3 & \hlmath{5} \\ 4 & \hlmath{7} \\ 5 & \hlmath{9}\end{array}
Sorted data2pos 13pos 25pos 37pos 49pos 5

Step 3 — Middle position

Find the middle position.

p=(5+1)/2=3p=( 5 + 1 )/ 2 = \hl{3}
Position 3 is the middle2pos 13pos 25pos 37pos 49pos 5middle

Step 4 — Read the middle value

Read the value at the middle position.

middlevalue=5middle value= \hl{5}
Middle value is 52pos 13pos 25pos 37pos 49pos 5middle

Step 5 — Median

The median is the middle value.

median=5median= \hl{5}
Middle value is 52pos 13pos 25pos 37pos 49pos 5middle
median Sort the data. For n values: - n odd: median = value at position (n+1)/2 - n even: median = average of positions n/2 and n/2+1