Question

I need all answers of my third question ​

Answer 1

$\large \star \: \mathtt{given : }$

Scores - 58 , 72 , 89 , 105 , 95

$\large \frak{formula : } \\ \\ \mapsto \underline{\boxed{ \sf \: avarage = \frac{sum \: \: of \: \: observations}{no. \: \: of \: \: observations} }} \\ \\ \\ \tt \implies \: avarage = \frac{58 + 72 +89 + 105 +95 }{5} \\ \\ \\ \tt \implies \: avarage = \frac{419}{5} \\ \\ \\ \large \underline{ \underline{ \star \: \: \sf \: avarage = 83.8}}$

☞︎︎︎ Median

• Ascending Order :

58 , 72 , 89 , 95 , 105

• Number of observation (n) = 5

$\\ \large \star \: \tt \: formula : \\ \\ \rm \: median : \\ \\ \sf \leadsto \underline{ \boxed{ \sf \: = \frac{{ \left( \dfrac{n}{2} \right) }^{th}observation + { \left( \dfrac{n + 1}{2} \right) }^{th}observation }{2} }}$

$\sf \implies { { \sf \: \dfrac{{ \left( \dfrac{10}{2} \right) }^{th}observation + { \left( \dfrac{10+ 1}{2} \right) }^{th}observation }{2} }} \\ \\ \\ \sf \implies { { \sf \: \dfrac{{ \left( 5 \right) }^{th}observation + { \left( 5 + 1 \right) }^{th}observation }{2} }} \\ \\ \\ \sf \implies { { \sf \: \dfrac{{ \left( 5 \right) }^{th}observation + { \left( 6 \right) }^{th}observation }{2} }}$

• There is no 6th observation..

$\\ \implies \sf \: median = \frac{6}{2} \: \: observation \\ \\ \ \sf{ \: median = 3 \: \: obsrvation} \\ \\ \large \boxed{ \sf \: median = 89}$

Similarly :

2) Observations = 12 , 42 , 15 , 36 , 50 , 33 , 25

No. of observation (n) = 7

( odd value )

• Ascending Order

12 , 15 , 25 , 33 , 36 , 42 , 50

$\large \mathfrak{formula : } \\ \\ \sf \leadsto \: {\boxed{\boxed{ \sf \frac{(n + 1 {)}^{th} \: observation}{2} }}}$

$\sf \implies median = \dfrac{7 + 1}{2} \: \: observation \\ \\ \sf median = \frac{8}{2} \: \: observation \\ \\ \sf \: median = 4th \: \: observation \\ \\ \\ \large\underline{ \underline{ \sf \: median =33 }}$

3) Mode

Observation = 14 , 25 , 18 , 14 , 36 , 13 , 14

We see ,

$\\ \sf \: 14 \: \: occurs \: \: most \: \: frequently$

• Mode = 14