Question

The scores in mathematics test (out of 25) of 15 students are as follows: 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, and 20. Find the mode and median of this data. Are they saml​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

The scores in mathematics test(out of 25) of 15 students are as follows :

$\sf 19, \: 25, \: 23, \: 20, \: 9, \: 20, \: 15, \: 10, \: 5, \: 16, \: 25, \: 20, \: 24, \: 12, \: 20$

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Mode \: and \: median \: of \: this \: data = \: ?$

$\sf \implies Are \: they \: same \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf First \: of \: all \: arrange \: the \: data \: in \: assending \: order.$

$\sf \underline{5, \: 9, \: 10, \: 12, \: 15, \: 16, \: 19, \: 20, \: 20, \: 20, \: 20, \: 23, \: 24, \: 25, \: 25}$

$\bf Now, finding \: the \: mode :$

$\sf Mode\: is\: the\: maximum\: occuring \:observation.$

$\sf \implies Since, 20 \: occurs \: 4 \: times.$

$\sf \underline{Therefore, mode \: of \: the \: given \: data \: is \: \bf 20. }$

$\bf Now, finding \: the \: medium :$

$\sf Here \: number \: of \: observations (N )=15$

$\sf Medium \: will \: be \: \dfrac{N + 1^{th}}{2} \: term$

$\sf \implies Medium = \dfrac{15 + 1^{th}}{2} \: term$

$\sf \implies Medium = \cancel{\dfrac{16^{th}}{2}} \: term$

$\sf \implies Therefore, \: medium = 8^{th} \: term$

$\sf The \: 8^{th} \: term \: is \: 20.$

$\sf \implies \: So, the \: medium \: is \: \bf20.$

$\bf Now, comparing \: mode \: and \: medium.$

$\sf \implies 20 = 20$

$\sf \implies Mode = Medium$

$\underline{\boxed{ \bf \red{Therefore, mode \: and \: medium \: are \: same.}}}$