Question

4 In the mathematics test given to 15 students the following marks (out
of 100) are recorded
41, 39, 48, 52, 46, 62, 54, 40,96; 52, 98, 40, 42, 52, 60
Find the mean median and mode of the data.​

Answer 1

$\sf\huge{solution}$

$\huge\sf \underline\purple{given}$

$\bigstar \: \sf \pink{total \: number \: of \: students = 15}$

$\bigstar \: \sf \pink{total \: marks \: out \: of \: 100 =} \green{ 41 , 39 , 48, 52 ,46 ,62 ,54 ,40 ,96 ,52 ,98 ,40 ,42 ,52 ,60}$

$\huge\sf\underline\purple{find}$

$\bigstar \: \sf\pink{mean} \\ \bigstar \: \sf \pink{ median} \\ \bigstar \: \sf \pink{ mode}$

$\huge\underline\bold{mean}$

$\\ \color{red}as \: we \: know - \\ \bold{ \star \: mean = \frac{sum \: of \: observations}{total \: number \: of \: observations}}$

$\bold{\frac { \: = \: 41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60} {15}}$

$\bold{\frac{822}{15} = 54.8}$

$\underline{\fbox{mean = 54.8}}$

$\huge\underline\bold{median}$

$\red{ \dagger \: arrange \: them \: in \: ascending \: order}$

$= \green{ 39 , 40, 40 ,41 ,42 ,46 ,48 ,52 ,52 ,52 ,54,60 ,62 ,96,98}$

$\bold{\star \: number \: of \: observations = n = 15(odd)}$

$\red{as \: we \: know \: the \: formulae} \\ \star \: \bold{ median = (\frac{n + 1}{2})^{th} observation}$

$\bold{= (\frac{15 + 1}{2})^{th} observation}$

$\bold{ = {8}^{th} observation}$

$\underline{\fbox{median = 52}}$

$\huge\underline\bold{mode}$

$= \green{ 39 , 40, 40 ,41 ,42 ,46 ,48 ,52 ,52 ,52 ,54,60 ,62 ,96,98}$

$\sf\red{here - } \\ \circ \: 39 \: occurs \: 1 \: time \\ \circ \: 40 \: occurs \: 2 \: time \\ \circ \: 41 \: occurs \: 1 \: time \\ \circ \: 42 \: occurs \: 1 \: time \\ \circ \: 46 \: occurs \: 1 \: time \\ \circ \: 48 \: occurs \: 1 \: time \\ \circ \: 52 \: occurs \: 3 \: time \\ \circ \: 54 \: occurs \: 1 \: time \\ \circ \: 60 \: occurs \: 1 \: time \\ \circ \: 62 \: occurs \: 1 \: time \\ \circ \: 62 \: occurs \: 1 \: time$

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@Sia1234567