Question

20. Find median of 2/3,4/5, 1/2, 3/4, 6/5​

Answer 1

Given

• $\sf{Observation= \dfrac{ 2}{3},\dfrac{4}{5}, \dfrac{1}{2},\dfrac{3}{4}, \dfrac{ 6}{5} }$

To Find

• Median

Formula used

$\begin{gathered}\\\begin{gathered} \sf{Median}\begin{cases}\sf{\:\;\; value \: of \: \left( \frac{n+1}{2}\right)^{th} observations \: if \: n \: is \: odd} \\ \\\sf{\;\;\; \cfrac{value \: of \: \left( \frac{n}{2}\right)^{th} observations + value \: of \: \left( \frac{n+1}{2}\right)^{th} observations} {2}\ if \ n \ is \ odd}\end{cases}\end{gathered}\end{gathered}$

Solution

${\sf First ~we ~convert ~the~ Observation \: \: \dfrac{ 2}{3},\dfrac{4}{5}, \dfrac{1}{2},\dfrac{3}{4}, \dfrac{ 6}{5} \: into \: like \: fraction}$

Converting unlike fractions to like fractions:

1. First find the LCM (lowest common multiple) of the denominators of the given fractions.
2. Then convert each fraction to its equivalent fraction with denominator equal to the LCM obtained in Step 1.

LCM of Denominator = 3×4×5=60

$\\\dashrightarrow\sf \cfrac{2}{3} \times \cfrac{20}{20} = \dfrac{40}{60}$

$\dashrightarrow\sf \cfrac{4}{5} \times \cfrac{12}{12} = \dfrac{48}{60}$

$\dashrightarrow\sf \cfrac{1}{2} \times \cfrac{30}{30} = \dfrac{30}{60}$

$\dashrightarrow\sf \cfrac{3}{4} \times \cfrac{15}{15} = \dfrac{45}{60}$

$\dashrightarrow\sf \cfrac{5}{6} \times \cfrac{10}{10} = \dfrac{50}{60}$

$\\ \sf The~~ Observation~~ are~~ \dfrac{40}{60}~~\dfrac{48}{60}~~\dfrac{30}{60}~~\dfrac{45}{60}~~\dfrac{50}{60}$

Let Arranging the Observation in Ascending Oder

$\\\sf \: observation = \dfrac{30}{60},\dfrac{40}{60},\dfrac{45}{60},\dfrac{48}{60},\dfrac{50}{60}$

$\\\gray{\sf{\:\;\;Median = value \: of \: \left( \frac{n+1}{2}\right)^{th} observations \: if \: n \: is \: odd}}$

Where n is number of observations:

$\\\sf{\:\;\;Median = value \: of \: \left( \frac{5+1}{2}\right)^{th} observations }$

$\sf{\:\;\;Median = value \: of \: \left( \dfrac{6}{2}\right)^{th} observations }$

$\\\sf{\:\;\;Median = value \: of \: 3^{th} observations }$

The 3rd term of observations is 45/60.

$~~~~~~~~~~~~~~~~~~~~~~~\\~~~\boxed{\bf Hance, \: Median = \purple{\dfrac{ 45}{60}}}$