Population of city A, B and C from 1981 - 2011 . Choose the correct statement:

Population in city A is increasing in each decade from 1981 to 2001 whereas city B shows a decline from 1981 to 1991 and then it increases from 1991 to 2011 .

City A shows the increase in population from 1981 to 2011 and city C does not show the increase likewise.

City C shows continuous decline in population in various decades whereas city B shows increase.

City B shows a continuous decline in population from 1981 - 2011 whereas city A shows an increase.

The expenditure of a municipal corporation of a city in different sectors is given below: Sector Expenditure (in Lakh) Education 350 Health services 480 Beautification 130 Surface transport 240 Others 600 Draw a pie-chart to represent the above data.

In this question, we are given data on expenditure of a municipal corporation of a city in different sectors and we have to draw a pie chart for this data. For this, we will first change the expenditure of different sectors into central angles (degrees) for a circle using the formula: Central angle of component = component value sum of all components × 360 ° The sum of all components = 1800 Sector Expenditure (in Lakh) Sector angle Education 350 350 1800 × 360 ° = 70 ° Health services 480 480 1800 × 360 ° = 96 ° Beautification 130 130 1800 × 360 ° = 26 ° Surface transport 240 240 1800 × 360 ° = 48 ° Others 600 600 1800 × 360 ° = 120 ° Now, let us understand the steps involved in making pie charts. Step 1: Draw a circle of an appropriate radius. Step 2: Draw a vertical radius of the circle drawn in step 1. Step 3: Choose the largest central angle. Here, the largest central angle for other sectors is 120 ° . So, for other sectors draw a sector with central angle 120 ° in such a way that one of its radii coincide with the radius drawn in step 2 and another radius is in its counter-clockwise direction. Step 4: Construct other sectors representing other items in the clockwise sense in descending order of magnitude of their central angles. Step 5: Shade the sectors with different patterns and label them. Now, let us draw pie charts using the above steps.

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution: Monthly Consumption (in units) 140 – 160 160 – 180 180 – 200 200 – 220 220 – 240 240 – 260 260 - 280 Number of Families 3 8 15 40 50 30 10 Prepare a ‘more than type’ ogive for the given frequency distribution.

The frequency distribution table of more than type is as follows: Height (in cm ) (lower class limit) Cumulative frequency ( c f ) More than 140 3 + 153 = 156 More than 160 8 + 145 = 153 More than 180 15 + 130 = 145 More than 200 40 + 90 = 130 More than 220 50 + 40 = 90 More than 240 30 + 10 = 40 More than 260 10 Taking the lower class limits of on x -axis and their respective cumulative frequencies on y -axis, its ogive can be drawn as follows:

The heights of 50 girls of Class X of a school are recorded as follows: Height (in cm ) 135 - 140 140 – 145 145 – 150 150 – 155 155 – 160 160 – 165 No of Students 5 8 9 12 14 2 Draw a ‘more than type’ ogive for the above data.

The frequency distribution table of more than type is as follows: Height (in cm ) (lower class limit) Cumulative frequency ( c f ) More than 135 5 + 45 = 50 More than 140 8 + 37 = 45 More than 145 9 + 28 = 37 More than 150 12 + 16 = 28 More than 155 14 + 2 = 16 More than 160 2 Taking lower class limits of on x -axis and their respective cumulative frequencies on y -axis, its ogive can be drawn as follows:

During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight (in kg ) Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph verify the result by using the formula.

The cumulative frequency distributions of less than type is given as Weight (in kg ) upper class limits Number of students (cumulative frequency) Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Now, on x - axis we take upper class limits of class intervals and their respective cumulative frequencies on y - axis we can draw its ogive as follows : Now mark the point A whose ordinate is 17 . 5 its abscissa is 46 . 5 . So median of this data is 46 . 5 . We can see from the table that difference between two consecutive upper-class limits is 2 . Now we have to obtain class marks with their respective frequencies as below : Weight (in kg) Frequency (f) Cumulative frequency Less than 38 0 0 38 - 40 3 - 0 = 3 3 40 - 42 5 - 3 = 2 5 42 - 44 9 - 5 = 4 9 44 - 46 14 - 9 = 5 14 46 - 48 28 - 14 = 14 28 48 - 50 32 - 28 = 4 32 50 - 52 35 - 32 = 3 35 Total ( n ) 35 Here, n = 35 . So, n 2 = 17.5 Now the cumulative frequency just greater than n 2 i . e . , 35 2 = 17.5 is 28 . It belongs to class interval 46 – 48 So, Median class = 46 – 48 Lower class limit ( l ) of median class = 46 Frequency ( f ) of median class = 14 Cumulative frequency ( c f ) of class preceding median class = 14 Class size ( h ) = 2 M e d i a n = l + n 2 - c f f × h = 46 + 17.5 - 14 14 × 2 = 46 + 3.5 7 = 46 + 0.5 = 46 . 5 So, median of this data is 46 . 5 . Hence, value of median is verified.

The table given below shows the weekly expenditures on food of some households in a locality Weekly expenditure (in Rs ) Number of house holds 100 – 200 5 200 - 300 6 300 – 400 11 400 - 500 13 500 – 600 5 600 – 700 4 700 – 800 3 800 – 900 2 Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.

The frequency distribution table of less than type is as follows: Weekly expenditure (in Rs ) (upper class limits) Cumulative frequency (cf) Less than 200 5 Less than 300 5 + 6 = 11 Less than 400 11 + 11 = 22 Less than 500 22 + 13 = 35 Less than 600 35 + 5 = 40 Less than 700 40 + 4 = 44 Less than 800 44 + 3 = 47 Less than 900 47 + 2 = 49 Taking the lower class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be obtained as follows Now, The frequency distribution table of more than type is as follows: Weekly expenditure (in Rs ) (lower class limits) Cumulative frequency ( c f ) More than 100 44 + 5 = 49 More than 200 38 + 6 = 44 More than 300 27 + 11 = 38 More than 400 14 + 13 = 27 More than 500 9 + 5 = 14 More than 600 5 + 4 = 9 More than 700 2 + 3 = 5 More than 800 2 Taking the lower class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be obtained as follows:

EASY

Earn 100

Which of the following statements is true about histograms?

50% studentsanswered this correctly

Important Questions on Introduction to Graphs

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Population of city A, B and C from $1981 - 2011 .$

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Choose the correct statement:

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

In a factory, there are $39$ workers who have been categorised into five groups ( $A, B, C, D, E$ ) on the basis of the range of their daily wages (in multiples of $₹ 100$ ). The distribution is presented through a Histogram shown below:

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What is the ratio of the number of employees whose daily wages are $₹ 200$ or more but less than $₹ 400$ to that of the number of employees whose daily wages are $₹ 400$ or more but less than $₹ 600$ ?

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The given graph shows the weights of students in a school on a particular day.

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The number of students weighing less than $50 kg$ is what percent less than the number of students weighing $55 kg$ or more?

EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The modal class of the frequency distribution given below is _____.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$7$	$15$	$13$	$17$	$10$

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Study the graph and answer the question,

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The number of workers in the factory whose daily wages are $₹ 450$ or more but less than $₹ 600$ is:

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The given graph shows the marks obtained by the students in an examination.

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The numbers of students who obtained less than $300$ marks is what percent more than the number of students who obtained $350$ or more marks?

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The expenditure of a municipal corporation of a city in different sectors is given below:

Sector	Expenditure (in Lakh)
Education	$350$
Health services	$480$
Beautification	$130$
Surface transport	$240$
Others	$600$

Draw a pie-chart to represent the above data.

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

Monthly Consumption (in units)	$140 - 160$	$160 - 180$	$180 - 200$	$200 - 220$	$220 - 240$	$240 - 260$	$260 - 280$
Number of Families	$3$	$8$	$15$	$40$	$50$	$30$	$10$

Prepare a ‘more than type’ ogive for the given frequency distribution.

EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Christo collected details of a dealer who sells used cars of different ranges. What is the price range of the minimum number of cars sold?

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MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The heights of $50$ girls of Class $X$ of a school are recorded as follows:

Height (in $cm$ )	$135 - 140$	$140 - 145$	$145 - 150$	$150 - 155$	$155 - 160$	$160 - 165$
No of Students	$5$	$8$	$9$	$12$	$14$	$2$

Draw a ‘more than type’ ogive for the above data.

HARD

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Draw a histogram for the given data, using the frequency table and answer the following question.

The weekly wages (in $₹$ ) of $30$ workers in a factory are. $830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840$

Which group has the maximum number of workers?

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

During the medical check-up of $35$ students of a class, their weights were recorded as follows:

Weight (in $kg$ )	Number of students
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph verify the result by using the formula.

EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Christo collected details of a dealer who sell used cars of different ranges. What is the price range of the maximum number of cars sold?

Question Image

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The table given below shows the weekly expenditures on food of some households in a locality

Weekly expenditure (in $Rs$ )	Number of house holds
$100 - 200$	$5$
$200 - 300$	$6$
$300 - 400$	$11$
$400 - 500$	$13$
$500 - 600$	$5$
$600 - 700$	$4$
$700 - 800$	$3$
$800 - 900$	$2$

Draw a ‘less than type ogive’ and a ‘more than type ogive’ for this distribution.

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

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The histogram shows the distance travelled by all the subject teachers, everyday, from their house to school. If all the math teachers travel less than 20 km, then can you tell how many math teachers are there in the school?

EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Math scores of 28 students were recorded as follows.

They were also graded, based on their marks. Identify the correct histogram which represents the below given table.

No of Students	6	7	10	5
Marks Scored	60 – 70	70 – 80	80 – 90	90 - 100
Grades	B	B+	A	O

EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Mahesh’s father needs O + ve blood; from the given data can you tell us how many donors might be available to donate blood?

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EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

In an exhibition, Rekha counted all the jewellery items which had red rubies in them. According to the given histogram, there are _____ numbers of jewellery items which have red rubies in them.

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EASY

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

Given below is the efficiency of the delivery bikes (in km/litre) of a particular pizza shop.

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How many bikes have the highest efficiency?

MEDIUM

Mathematics>Statistics>Introduction to Graphs>Basic Graphical Representations

The given table represents the runs scored by Vishal in his interschool cricket premier league.

35	23	80	76	111
57	43	15	63	82
0	12	101	2	11
67	125	58	14	97
53	73	89	42	8

Identify the correct histogram which represents the given table.

Which of the following statements is true about histograms?

Important Questions on Introduction to Graphs

35

23

80

76

111

57

43

15

63

82

0

12

101

2

11

67

125

58

14

97

53

73

89

42

8

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