Tag: histograms and frequency distribution diagrams

Given series of numbers is already arranged in ascending order.
Thus median is the centre value $ = 20 $
First Quartile $ {Q} _{1} $ will be the mid value of the observations to the left of $ 20 $ which is $ 9 $. 
Similarly, Third Quartile $ {Q} _{3} $ will be the mid value of the observations to the right of $ 20 $ which is $ 34 $.
And Quartile deviation will be $ \dfrac {{Q} _{3} - {Q} _{1}}{2} = \dfrac {34-9}{2} = \dfrac {25}{2} = 12.5 $.

use:  M.D.$=\displaystyle \frac{4}{4}\sigma ,Q.D=\frac{2}{3}\sigma $ $\displaystyle \Rightarrow \frac{M.D.}{Q.D}=\frac{6}{5}\Rightarrow Q.D.=\frac{5}{6}\left ( M.D. \right )$


$MD=\frac { 4 }{ 5 } \times \sigma \quad ,\quad QD=\frac { 2 }{ 3 } \times \sigma \quad ,\quad \ \frac { MD }{ QD } =\frac { 6 }{ 5 } ,\quad QD\quad =\quad \frac { 5\times 15 }{ 6 } =12.5$

Lower Quartile $ {Q} _{1} = 4 $

Upper Quartile $ {Q} _{3} = 12 $

And Quartile deviation will be $ \frac {{Q} _{3} - {Q} _{1}}{2} = \frac {12-4}{2} = \frac {8}{2} = 4 $

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion.