Question 1196678

given:
{{{40.40}}}|{{{5.18}}}|{{{32.59}}}|{{{47.01}}}
{{{37.12}}}|{{{34.61}}}|{{{63.44}}}|{{{51.53}}}
{{{57.32}}}|{{{81.13}}}|{{{47.50}}}|{{{11.65}}}
{{{21.83}}}|{{{42.21}}}|{{{38.77}}}|{{{32.05}}}
{{{76.72}}}|{{{72.80}}}|{{{46.93}}}|{{{65.45}}}


Order your data set from lowest to highest values

{{{4.61}}}, {{{5.18}}}, {{{11.65}}}, {{{21.83}}}, {{{32.05}}}, {{{32.59}}}, {{{37.13}}}, {{{38.77}}}, {{{40.40}}}, {{{42.21}}},{{{ 46.93}}}, {{{47.01}}}, {{{47.50}}}, {{{51.53}}},{{{ 57.32}}},{{{ 63.44}}}, {{{65.45}}}, {{{72.80}}}, {{{76.72}}},{{{ 81.13}}}


Find the median (add all and divide the sum by number of data). This is the second quartile {{{Q2}}}.

{{{Q2= (42.21+46.93)/2=44.57}}}

At {{{Q2}}} split the ordered data set into two halves.

{{{4.61}}}, {{{5.18}}}, {{{11.65}}}, {{{21.83}}}, {{{32.05}}}, {{{32.59}}}, {{{37.13}}}, {{{38.77}}}, {{{40.40}}}, {{{42.21}}}

{{{ 46.93}}}, {{{47.01}}}, {{{47.50}}}, {{{51.53}}},{{{ 57.32}}},{{{ 63.44}}}, {{{65.45}}}, {{{72.80}}}, {{{76.72}}},{{{ 81.13}}}




The lower quartile {{{Q1}}} is the median of the lower half of the data.

{{{4.61}}}, {{{5.18}}}, {{{11.65}}}, {{{21.83}}}, {{{32.05}}}, {{{32.59}}}, {{{37.13}}}, {{{38.77}}}, {{{40.40}}}, {{{42.21}}}


{{{Q1 = (32.05+32.59)/2=32.32 }}}}


The upper quartile {{{Q3}}} is the median of the upper half of the data.

{{{ 46.93}}}, {{{47.01}}}, {{{47.50}}}, {{{51.53}}},{{{ 57.32}}},{{{ 63.44}}}, {{{65.45}}}, {{{72.80}}}, {{{76.72}}},{{{ 81.13}}}


{{{Q3=(57.32+63.44)/2=60.38}}}

Interquartile Range: 
{{{IQR = Q3 - Q1}}}
{{{IQR =60.38- 32.32 =28.06}}}