4 Marks Each

Question 14 Marks

The mean and standard deviation of the marks obtained by $100$ students in the test of $60$ marks are $40$ and $5.1$ respectively. Later on, it was known that one of the students scored $40$ Marks of but by mistake it was taken as $50$. Find the correct marks value of the standard deviation of the marks.

Answer

Standard Deviation $=5$ Marks

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Question 24 Marks

The number of students who scored $85$ or more marks out of $100$ marks in the subject of Statistics in the $12th$ board exam for last ten years in two schools are given below.

Year	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
School $A$	$17$	$13$	$14$	$26$	$53$	$29$	$79$	$36$	$49$	$84$
School $B$	$22$	$37$	$10$	$20$	$56$	$52$	$37$	$14$	$48$	$4$

Find the coefficients of variation of the number of students of both the schools and compare them.

Answer

School $A$ : Coefficient of Variation $=61.1 \%$;
School $B$: Coefficient of Variation $=58.47 \%$
The marks of students in school $B$ has less variation.

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Question 34 Marks

The mean and standard deviation of a sample of size $15$ are $3.5$ and $3$ respectively and that of another sample of size $22$ are $4.7$ and $4$ respectively.
Obtain the combined standard deviation from this information.

Answer

Combined Standard Deviation $=3.68$

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Question 44 Marks