5 Mark Each

Question 15 Marks

$200$ students of science stream cast their votes in an election of a higher secondary school and $40 \%$ of them were girls. The numbers of students in standard $11$ and $12$ were equal. $10 \%$ of the votes cast were invalid. The proportion of valid votes cast in standard $11$ and $12$ was $7: 8$. Of them, $40$ girls were from standard $11$ and $38$ girls were from standard $12$ . The number of invalid votes of boys and girls of standard $12$ were equal. Present the data in a tabular form.

Answer

Table showing class and gender wise number of votes given by students:

Vote	Standard
	$11$			$12$			Total
	Boys	Girss	Total	Boys	Girls	Total	Boys	Girls	Total
Valid vote	$44$	$40$	$84$	$58$	$38$	$96$	$102$	$78$	$180$
Invalid vote	$16$	$-$	$16$	$2$	$2$	$4$	$18$	$2$	$20$
Total	$60$	$40$	$100$	$60$	$40$	$100$	$120$	$80$	$200$ $a$

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Question 25 Marks

The data of retail price (in $₹$) of an item for $40$ days are as follows. Prepare an inclusive frequency distribution having classlength 1 and one class $19-19.99$.
$\text{20.75 21.30 20.50 18.20 17.00 17.65 18.70 21.87}$
$\text{19.40 21.30 18.35 22.45 23.15 22.95 22.18 20.26}$
$\text{22.25 23.43 24.20 23.80 23.50 23.60 24.80 24.10}$
$\text{23.45 23.56 23.95 23.00 23.80 24.30 24.52 18.65}$
$\text{18.40 17.42 18.10 23.60 18.65 24.35 24.15 22.18}$

Answer

Inclusive frequency distribution of retail price $(₹)$ of an item for $40$ days:

Price	$17-17.99$	$18-18.99$	$19-19.99$	$20-20.99$	$21-21.99$	$22-22.99$	$23-23.99$	$24-24.99$	Total
No. of days	$3$	$7$	$1$	$3$	$3$	$5$	$11$	$7$	$40$

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Question 35 Marks

Marks obtained by $50$ students in a test of $50$ marks are as follows :
$\text{16 18 27 31 43 25 28 30 29 15}$
$\text{20 27 31 34 39 41 22 28 31 16}$
$\text{21 29 38 24 30 24 26 17 30 22}$
$\text{28 35 23 18 24 32 37 27 32 38}$
$\text{19 25 33 25 29 25 34 45 26 24}$
$(i)$ From these data, prepare a frequency distribution by taking class length $5$ .
$(ii)$ Obtain 'less than' and 'more than' type cumulative frequency distribution.
$(iii)$ If standard of passing is $20$ marks, then how many students have failed ?
$(iv)$ If at least $30$ marks are required to get first class, find the number of students in this category.

Answer

$(i)$ Frequency distribution of marks obtained by students in a test of $50$ marks.

Marks	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$	$40-45$	$45-50$	Total
No. of students	$7$	$9$	$15$	$11$	$5$	$2$	$1$	$50$

$(ii)$ 'Less than' type cumulative frequency distribution :

Less than marks	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
Cumulative frequency	$0$	$7$	$16$	$31$	$42$	$47$	$49$	$50$

'More than' type cumulative frequency distribution:

More than marks	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
Cumulative frequency	$50$	$43$	$34$	$19$	$8$	$3$	$1$	$0$

$(iii)$ $7$ $(iv)$ $19$

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Question 45 Marks

The frequency distribution of monthly saving of $400$ persons is as follows :

Saving $(₹)$	$0-1000$	$1001-2000$	$2001-3000$	$3001-4000$	$4001-6000$	$6001$ and more
No. of persons	$25$	$40$	$50$	$150$	$90$	$45$

Answer the following questions from the frequency distribution :
$(i)$ Find the midvalue of the third class.
$(ii)$ Find the lower boundry point of the open ended class.
$(iii)$ Find number of persons having the saving more than $₹ 1000$ and less than $₹ 4001$.
$(iv)$ Find the class length of the fourth class.
$(v)$ Find number of persons having the saving of $₹ 4000$ or less.

Answer

$(i)$ $2500.5$
$(ii)$ $6000.5$
$(iii)$ $240$
$(iv)$ $1000$
$(v)$ $265$

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