3 Marks Question

Question 13 Marks

Draw a histogram for the daily earning of 30 drug stores in the following table:

Daily earning (in ₹):	$450-500$	$500-550$	$550-600$	$600-650$	$650-700$
Number of stores:	$16$	$10$	$7$	$3$	$1$

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Question 23 Marks

Read the following bar graph and answer the following questions:
$i.$ What is the information given by the bar graph?
$ii.$ State each of the following whether true or false.
$a.$ The number of government companies in $1957$ is that of $1982$ is $1 : 9$.
$b.$ The number of government companies has decreased over the year $1957$ to $1983$.

Answer

$i.$ The bar graph represents the number of government companies in India during some years.
$a.$ The number of companies in $1957$ was $50$ and the number of companies in $1982$ was $375$.
Their ratio in that order is $50 : 375 = 2 : 15$
Hence, the statement is false.
$b.$ The height of the bar graphs increases over the years $1957$ to $1983$.
Hence, the statement is false.
$2 : 15$

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Question 33 Marks

The following bar graph shows the results of an annual examination in a secondary school. Read the bar graph and choose the correct alternative in each of the following:

$i.$ The pair of classes in which the results of boys and girls are inversely proportional are:
$a. VI, VIII$
$b. VI, IX$
$c. VII, IX$
$d. VIII, X$
$ii.$ The class having the lowest failure rate of girls is:
$a. VI$
$b. X$
$c. IX$
$d. VIII$
$iii.$ The class having the lowest pass rate of students is:
$a. VI$
$b. VII$
$c. VIII$
$d. IX$

Answer

$i.$ The pair of classes in which the results of boys and girls are inversely proportional are $VI$ and $IX$.
$ii.$ The lowest failure rate of girls is same to the highest pass rate.
Hence, the class having the lowest failure rate of girls is $VII ($the height of the bar corresponding to girls for this class is maximum$)$.
$iii.$ The sum of the heights of the bars for boys and girls in class $VII$ is minimum, which is $95 + 40 = 135$.
Hence, the class having the lowest pass rate is $VII$.
Hence, the correct choice is $(b)$.

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Question 43 Marks

Construct a histogram for the following data:

Monthly School fee (in ₹):	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$	$180-210$	$210-240$
No of schools	$5$	$12$	$14$	$18$	$10$	$9$	$4$

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Question 53 Marks

The following is the distribution of total household expenditure (in ₹) of manual worker in a city:

Expenditure (in ₹):	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$	$350-400$	$400-450$	$450-500$
No. of manual workers:	$25$	$40$	$33$	$28$	$30$	$22$	$16$	$8$

Draw a histogram and a frequency polygon representing the above data.

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Question 63 Marks

Read the bar graph given in and answer the following questions:
$i.$ What information is given by the bar graph?
$ii.$ What was the crop$-$production of rice in $1970–71?$
$iii.$ What is the difference between the maximum and minimum production of rice?

Answer

$ i.$ The bar graph represents the production of the rice crop in India in different years.
$ii.$ According to the height of the $3^{\text {rd }}$ bar from the left, the crop$-$production of rice in $1970-71$ is $42.5$ lakh tones.
$ iii.$ The maximum product of rice is $55$ lakh tones $($height of the $4^{\text {th }}$ bar from the left$)$ in the year $1980-81$ and the minimum product of rice is $22$ lakh tones $($height of the $1^{\text {st }}$ bar from the left$)$ in the year $1950-51$.
Hence, the difference between maximum and minimum production of rice $($in lakh tones$)$ is $55-22=33$

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Question 73 Marks

The monthly profits (in ₹) of $100$ shops are distributed as follows:

Profits per shop:	$0-50$	$50-100$	$100-150$	$150-200$	$200-250$	$250-300$
No. of shops:	$12$	$18$	$27$	$20$	$17$	$6$

Draw a histogram for the data and show the frequency polygon for it.

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Question 83 Marks

Read the following bar graph and answer the following questions:
$i.$ What information is given by the bar graph?
$ii.$ What was the production of cement in the year $1980–81$?
$iii.$ What are the minimum and maximum production of cement and corresponding years?

Answer

$i.$ The bar graph represents the industrial production of cement in different years in India.
$ii.$ According to the height of the $6^{th}$ bar from the left.
the production of cement in the year $1980–81$ was $186$ lakh tonnes.
$iii.$ According to the heights of the bars.
The minimum production of cement is $30$ lakh tonnes in the year $1950–51$ and the maximum production of cement is $232$ lakh tonnes in the year $1982–83$.

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Question 93 Marks

The distribution of height (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on the same axes.

Height (in cm):	$124$ to $128$	$128$ to $132$	$132$ to $136$	$136$ to $140$	$140$ to $144$	$144$ to $148$	$148$ to $152$	$152$ to $156$	$156$ to $160$	$160$ to $164$
No. of children:	$5$	$8$	$17$	$24$	$16$	$12$	$6$	$4$	$3$	$1$

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Question 103 Marks

Read the graph given in figure and answer the following question:
$i.$ What information is given by the bar given?

$ii.$ In which years the areas under the sugarcane crop were the maximum and the minimum?
$iii.$ State whether true or false:
The area under sugarcane crop in the year $1982–83$ is three times that of the year $1950–51$.

Answer

$i.$ The bar graph represents the areas $($in lakh hectares$)$ under sugarcane crop during different years in India.
$ii.$ It is seen from the bar graph that the area under the sugarcane crop is maximum in the year $1982–83$ and minimum in the year $1950–51$.
$iii.$ The area under the sugarcane crop in the years $1982–83$ and $1950-51$ are $34$ lakh hectares and $18$ lakh hectares respectively.
Clearly, $34$ is not equal to $3$ multiplied by $18$.
Hence, the statement is false.

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Maths 3 Marks Question

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