There are $$60$$ students in a class. The following is the frequency distribution of the marks obtained by the students in a testwhere, x is a positive integer. Find the mean and standard deviation of the marks.

Question

Infinity Learn · Accepted Answer

First find x as given total number of students is $$60$$ i.e.     x−$$2+x+x2+(x+1)2+2x+x+1$$    $$=60$$⇒    $$5x$$−$$2+x2+x2+1+2x+1$$    $$=60$$⇒    $$2x2+7x$$    $$=60$$⇒    $$2x2+7x$$−$$60$$    $$=0$$⇒    $$2x2+15x$$−$$8x$$−$$60$$    $$=0$$⇒    $$x(2x+15)$$−$$4(2x+15)$$    $$=0$$⇒    (2x+15)(x$$−$$4)    $$=0$$⇒    $$x=$$−$$152$$,x    $$=4$$⇒    $$x=4$$    $$($$∵x is positive $$)$$ Mean x¯$$=$$Σ$$fixiN=16860=2.8$$∴  Variance σ$$2=$$Σ$$fixi2N$$−$$(x$$¯$$)2=54660$$−$$(2.8)2$$ $$=9.1$$−$$7.84=1.26=1.12$$

Marks	0	1	2	3	4	5
Frequency	x-2	x	x²	(x+1)²	2x	x+1

Measurement	0 - 10	10 - 20	20 - 30	30 - 40
Frequency	1	3	4	2

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test
Marks 0 1 2 3 4 5
Frequency x-2 x x² (x+1)² 2x x+1
where, x is a positive integer. Find the mean and standard deviation of the marks.

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There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a testMarks012345Frequencyx-2xx2(x+1)22xx+1where, x is a positive integer. Find the mean and standard deviation of the marks.

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There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test
Marks 0 1 2 3 4 5
Frequency x-2 x x² (x+1)² 2x x+1
where, x is a positive integer. Find the mean and standard deviation of the marks.