Question

In a Mathematics test given to
15 students, the following marks (out of 100) are
recorded :
41. 39. 48, 52, 46, 02, 54, 40, 96,
52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.​

Answer 1

$\huge{\underline{\underline{\sf{\pink{Required\:Solution:}}}}}$

$\displaystyle{\rm{(i)}}$ Meαn

$\displaystyle{\sf{Mean\:=\: \dfrac{Sum\:of\:all\:the\:observations}{Total\:number\:of\:observations}}}$

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

$\displaystyle{\sf{=\: \dfrac{822}{15}}}$

$\large{\boxed{\bf{\orange{54.8}}}}$

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$\displaystyle{\rm{(ii)}}$ Mediαn

Arrαnging the given dαtα in descending order, we hαve

⠀⠀⠀⠀⠀98, 96, 62, 60, 54, 52, 52, 52,

⠀⠀⠀⠀⠀48, 46, 42, 41, 40, 40, 39

Number of observαtion (n) = 15, which is odd.

$\displaystyle{\sf{ \therefore Median = \big( \dfrac{n+1}{2} \big)^{th} observation.}}$

$\implies{\sf{ \:\:\:\:\:\:\:\:\:\:\: \big( \dfrac{15+1}{2} \big)^{th} observation.}}$

$\large{\boxed{\bf{\orange{8^{th} observation = 52}}}}$

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$\displaystyle{\rm{(ii)}}$ Mode

Arrαnging the given dαtα in descending order, we hαve

⠀⠀⠀⠀⠀98, 96, 62, 60, 54, 52, 52, 52,

⠀⠀⠀⠀⠀48, 46, 42, 41, 40, 40, 39

Here, 52 occurs most frequently (3 times)

$\large\implies{\boxed{\bf{ \therefore {\pink{Mode=52}}}}}$

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