Question

Following are the marks obtained by seven students of a class:
59, 68, 72, 49, 84, 92, 24
(i) Calculate the mean marks.
(ii) Find the mean marks if a student whose marks are 48, is also included.
(iii) What will be the mean marks, if a student whose marks is 72 is excluded?​

Answer 1

Answer:

Given;

The average marks of 40 students in an examination =34

It was found that one student had been wrongly entered as 62 instead of 26.

The marks of students in an examination=40*34=1360

62-26=36

1360-36=1324

After correction of marks the mean =1324/40

=33.1

After correction of marks the mean is 33.1

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Answer 2

$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\: Question\:1\::-\:\:\:}}}}}}$

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(i) Calculate the mean marks.

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$\star\small\sf\underline\green{Solution:-}$

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$\sf \: Mean \: marks = \dfrac{59 + 68 + 72 + 49 + 84 + 92 + 24}{7} \\\\ \\ \sf \: Mean \: marks = \cancel\frac{488}{7} \\\\ \\ \sf \: Mean \: marks = \large{\boxed{\bf\blue{64 \: marks }}}$

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$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\: Question\:2\::-\:\:\:}}}}}}$

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(ii) Find the mean marks if a student whose marks are 48, is also included.

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$\star\small\sf\underline\green{Solution:-}$

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If the marks of one more student with 48 marks is included, then the sum of the observations will be

$\: \: \: \: \: \: \sf = 59 + 68 + 72 + 49 + 84 + 92 + 24 + 48 \\ \\ \: \: \: \: \: \: \sf = 496 \\ \\ \sf \: Number \: of \: observations = 7 + 1 \\ \\ \sf \: Number \: of \: observations = \: \large{\boxed{\bf\blue{8 }}}$

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$\star\small\sf\underline\pink{Hence:-}$

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$\sf \: New \: mean = \cancel\dfrac{496}{8} \\ \\ \sf \: New \: mean = \large{\boxed{\bf\blue{62 \: marks }}}$

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$\underline{\underline{\underline{\underline{\mathfrak{\blue{ \:\:\: Question\:3\::-\:\:\:}}}}}}$

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(iii) What will be the mean marks, if a student whose marks is 72 is excluded?

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$\star\small\sf\underline\green{Solution:-}$

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$\: \: \: \: \: \: = 59 + 68 + 49 + 84 + 92 + 24 \\ \\ = 376 \\ \\ \sf \: Number \: of \: observations = 7 - 6 \\ \\ \sf \: Number \: of \: observations = \: \large{\boxed{\bf\blue{6 }}}$

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______________________

$\star\small\sf\underline\pink{Hence:-}$

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$\sf \: New \: mean = \cancel\dfrac{376}{6} \\ \\ \sf \: New \: mean = 62\dfrac{2}{3} \\ \\ \sf \: New \: mean = \large{\boxed{\bf\blue{62.67 \: marks }}}$