Question

24. A boy scored the following marks in various class tests during a year, each test
being marked out of 20:
15, 17, 16, 7, 9, 12, 14, 16, 3, 19, 12, 16
(i) Arrange the marks in ascending order. (ii) What are his modal marks?
(iii) What are his median marks?
(iv) What are his mean marks?
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Answer 1

AnswEr :

( i ) Arrange the marks in ascending order.

$\underline{\bigstar\:\textsf{Arrangement in Ascending Order :}}\\\\\textsf{3, 7, 9, 12, 12, 14, 15, 16, 16, 16, 17, 19}\\\\\longrightarrow\boxed{\sf Here, \:N = 12}$

$\rule{250}{1}$

( ii ) What are his modal marks?

$\textsf{Modal Marks will be \bf{16} \sf{since it occurred}} \\ \textsf{maximum times i.e. three times.}\\\\ \bullet \:\textsf{The mode is the number that appears} \\ \quad\textsf{most frequently in a set.} \\\bullet \:\textsf{A set of numbers may have one mode,}\\ \quad\textsf{more than one mode, or no mode at all.}$

$\rule{250}{1}$

( iii ) What are his median marks?

$:\implies \sf Median = \dfrac{Number \:of \: Observations}{2} \\\\\\:\implies \sf Median = \cancel\dfrac{12 \:terms}{2} \\ \\ \\:\implies \sf Median =6th \:term \\ \\ \\:\implies \pink{\sf Median =14}$

⠀

∴ Hence, Median Marks of boy will be 14.

$\rule{250}{1}$

( iv ) What are his mean marks?

$:\implies \sf Mean = \dfrac{Sum \:of \:Observations}{Number \:of \:Observations}\\\\\\:\implies \sf Mean = \dfrac{3+7+9+12+12+14+15+16+16+16+17+19}{12} \\\\\\:\implies \sf Mean = \cancel\dfrac{156}{12}\\\\\\:\implies \blue{\sf Mean =13}$

⠀

∴ Hence, Mean Marks of boy will be 13.

$\rule{250}{2}$

$\underline{\bigstar\:\textsf{Checking whether Given Data is Correct or Not :}}$

$\underline{\bf\dag\quad\textsf{Using Empirical Formula :}}\\\\\longrightarrow \sf{Mode = 3Median - 2Mean} \\\\\\\longrightarrow \sf{16 = [3(14) - 2(13)]} \\ \\\\\longrightarrow \sf{16 = [42 - 26]} \\ \\ \\\longrightarrow \red{\sf{16 = 16}}$

⠀

∴ It can be clearly observed that the given relationship is TRUE in this case.

Answer 2

Answer:

$\bold\green{Answer:}$

i)Arrange the marks in ascending order.

$\Rightarrow\tt 3, 7, 9, 12, 12, 14, 15, 16, 16, 16, 17 , 19 .$

_______________________

ii) What are his modal marks?

At first, Modal marks are the marks which are achieved frequently and most times.

$\because In\:the\: given \: marks\:used\:most\:times = 16$

$\therefore Modal\:number = 16$

________________________

iii)What are his median marks?

$\Rightarrow\tt Median\:marks=\frac{Number\:of\:terms}{2}$

$\Rightarrow\tt Median\:marks=\frac{12\:terms}{2}$

$\Rightarrow\tt Median\:marks=6th\:term$

$\Rightarrow\tt Median\:marks=14$

_________________________

iv)What are his mean marks?

$\Rightarrow\tt Mean\:marks=\frac{Sum\:of\:terms}{Number\:of\:terms}$

$\Rightarrow\tt Mean\:marks=\frac{3 + 7 + 9 + 12 + 12 + 14 + 15 + 16 + 16 + 16 + 17 + 19}{12}$

$\Rightarrow\tt Mean\:marks=\frac{156}{12}$

$\Rightarrow\tt Mean\:marks=13$