Which one of the following is not the graphical representation of statistical data?
- ABar graph
- BHistogram
- CFrequency polygon
- ✓Cumulative frequency distribution
Answer: D.
View full solution →Question types
Graphical Representation of Statistical Data [NEW] question types
76 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
76
Questions
6
Question groups
5
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01
M.C.Q
23 Q→02Assertion (A) & Reason (B) MCQ
5 Q→033 Marks Question
10 Q→044 Marks Questions
22 Q→05Case study (4 Marks)
4 Q→065 Marks Questions
12 Q→Sample Questions
Graphical Representation of Statistical Data [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the 'less than' type of ogive the cumulative frequency is plotted against
- Athe lower limit of the concerned class interval
- ✓the upper limit of the concerned class interval
- Cthe mid-value of the concerned class interval
- Dany value of the concerned class interval
Answer: B.
View full solution →In Fig. 17.4, total number of students in the year 2015 was
- A1160
- ✓1270
- C1380
- D1490
Answer: B.
View full solution →In Fig. 17.4, the ratio between the number of students in the year 2016 and 2017 was
- A107:145
- B127:145
- ✓29:36
- D107: 127
Answer: C.
View full solution →In Fig. 17.4, the minimum difference between the number of boys and girls in any year in the given period was
- A90
- ✓70
- C50
- D30
Answer: B.
View full solution →Statement-1 (A): To draw the histogram of a continuous frequency distribution when class marks of class intervals are given, it is assumed that the frequency corresponding to the class mark a is spread over the interval
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-3
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): The graphical representation of the frequency distribution
is as given in Fig.
Statement-2 (R): In a histogram, the areas of the rectangles are proportional to the frequencies.
| Marks: | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 100 |
| Number of students: | 10 | 15 | 20 | 25 |
Statement-2 (R): In a histogram, the areas of the rectangles are proportional to the frequencies.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1
- ✓Statement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: C.
View full solution →Statement-1 (A): In a histogram, the areas of each rectangle is proportional to the frequencies of its classes.
Statement-2 (R): In a histogram the lengths or heights of rectangles are proportional to the frequencies.
Statement-2 (R): In a histogram the lengths or heights of rectangles are proportional to the frequencies.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: C.
View full solution →Statement-1 (A): In a histogram, the area of each rectangle is proportional to the class size of the corresponding interval.
Statement-2 (R): To draw the histogram of a continuous frequency distribution with unequal class intervals, the frequencies of classes are adjusted by using the formula:
Adjusted frequency of a class $=\frac{\text { Minimum class size }}{\text { Class size }} \times$ Frequency of the class
Statement-2 (R): To draw the histogram of a continuous frequency distribution with unequal class intervals, the frequencies of classes are adjusted by using the formula:
Adjusted frequency of a class $=\frac{\text { Minimum class size }}{\text { Class size }} \times$ Frequency of the class
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- ✓Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): A bar graph is a pictorial representation of the numerical data by a number of rectangles of uniform width erected horizontally or vertically with equal spacing between them.
Statement-2 (R): In order to draw the histogram when mid-points of class intervals are given, it is assumed that the frequency corresponding to the variate value a (say) is spread over the interval $a-\frac{h}{2}$ to $a+\frac{h}{2}$, where h is the jump from one value to other.
Statement-2 (R): In order to draw the histogram when mid-points of class intervals are given, it is assumed that the frequency corresponding to the variate value a (say) is spread over the interval $a-\frac{h}{2}$ to $a+\frac{h}{2}$, where h is the jump from one value to other.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
- ✓Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-2
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: B.
View full solution →The monthly profits (in ₹) of 100 shops are distributed as follows:
Draw a histogram for the data and show the frequency polygon for it.
| Profits per shop: | 0-50 | 50-100 | 100-150 | 150-200 | 200-250 | 250-300 |
| No. of shops: | 12 | 18 | 27 | 20 | 17 | 6 |
The following is the distribution of total household expenditure (in ₹) of manual worker in a city:
Draw a histogram and a frequency polygon representing the above data.
| 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 |
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:
Read the bar graph and choose the correct alternative in each of the following:
- The pair of classes in which the results of boys and girls are inversely proportional are:
- VI, VIII
- VI, IX
- VII, IX
- VIII, X
- The class having the lowest failure rate of girls is:
- VI
- X
- IX
- VIII
- The class having the lowest pass rate of students is:
- VI
- VII
- VIII
- IX
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 tom 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 |
Read the graph given in figure and answer the following question: 
- What information is given by the bar given?
- In which years the areas under the sugarcane crop were the maximum and the minimum?
- State whether true or false:
The area under sugarcane crop in the year 1982–83 is three times that of the year 1950–51.
The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
- Construct a frequency distribution for these data, using a class interval of 10 seconds.
- Draw a histogram to represent the frequency distribution.
The production of saleable steel in some of the steel plants of our country during 1999 is given below:
Construct a bar graph to represent the above data on a graph paper by using the scale 1 big divisions = 20 thousand tones.
| Plant | Bhilai | Durgapur | Rourkela | Bokaro |
| Production (in thousands) | 160 | 80 | 200 | 150 |
The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below:
Construct a bar graph to represent the above data so that the bars are drawn horizontally.
| Refinery | Barauni | Koyali | Mathura | Mumbai | Florida |
| Production of oil (in lakh tonnes) | 30 | 70 | 40 | 45 | 25 |
The income and expenditure for 5 years of a family is given in the following data:
Represent the above data by a bar graph.
| Years | 1995–96 | 1996–97 | 1997–98 | 1998–99 | 1999–2000 |
| Income (Rs. In thousands) | 100 | 140 | 150 | 170 | 210 |
| Expenditure (Rs. in thousands) | 80 | 130 | 145 | 160 | 190 |
The following table shows the number of Maruti cars sold by five dealers in a particular month:
Represent the above information by a pictograph.
| Dealer | saya | Bagga links | D.D Motors | Bhasin Motors | Competent |
| Cars sold | 60 | 40 | 20 | 15 | 10 |
Read the following bar graph and answer the following questions:
(i) In which year was the difference between the sales of the scooters and the sales of cars the least?
(a) 2015(\quad$ (b) 2016(\quad$ (c) 2017(\quad$ (d) 2018
(ii) Total number of vehicles (scooters and cars) sold in the year 2015 and 2016 was
(a) 26,100$\quad$ (b) 28,500$\quad$ (c) 25,100$\quad$ (d) 27,500
(iii) The maximum difference between the sales of scooters and cars, in any year, in the given period was
(a) 1500$\quad$ (b) 1700$\quad$ (c) 1800$\quad$ (d) 2000
(iv) The total number of scooters sold in the four years was
(a) 26,000$\quad$ (b) 27,000$\quad$ (c) 31,000$\quad$ (d) 32,000
(v) The ratio between the total number of vehicles sold (scooters and cars) in the year 2016 and that in the year 2018.
(a) 41:46$\quad$ (b) 69:91$\quad$ (c) 147:182$\quad$ (d) 46:49
View full solution →(i) In which year was the difference between the sales of the scooters and the sales of cars the least?
(a) 2015(\quad$ (b) 2016(\quad$ (c) 2017(\quad$ (d) 2018
(ii) Total number of vehicles (scooters and cars) sold in the year 2015 and 2016 was
(a) 26,100$\quad$ (b) 28,500$\quad$ (c) 25,100$\quad$ (d) 27,500
(iii) The maximum difference between the sales of scooters and cars, in any year, in the given period was
(a) 1500$\quad$ (b) 1700$\quad$ (c) 1800$\quad$ (d) 2000
(iv) The total number of scooters sold in the four years was
(a) 26,000$\quad$ (b) 27,000$\quad$ (c) 31,000$\quad$ (d) 32,000
(v) The ratio between the total number of vehicles sold (scooters and cars) in the year 2016 and that in the year 2018.
(a) 41:46$\quad$ (b) 69:91$\quad$ (c) 147:182$\quad$ (d) 46:49
Population census in India is conducted every 10 years. The first complete census was taken in 1881 and the 15th decennial census was taken in 2011. The 16th decennial census was to be conducted in 2021 but due to COVID it will be taken in 2022. The data obtained from the census of a town has been represented by a bar graph shown in Fig. 17.2. It represents the number of persons in various age groups in the town. Observe the bar graph and answer the following questions:
(i) What is the total number of persons living in the town in the age-groups 10-15 and 60 - 65?
(a) 2000$\quad$ (b) 2200$\quad$ (c) 2100$\quad$ (d) 1900
(ii) How many persons are more in the age-group 10 - 15 than in the age group 30-35?
(a) 200$\quad$ (b) 250$\quad$ (c) 300$\quad$ (d) 350
(iii) What is the total population of the town?
(a) 6700$\quad$ (b) 6400$\quad$ (c) 7700$\quad$ (d) 6600
(iv) What is the number of persons in the age-group 60-65?
(a) 900$\quad$ (b) 750$\quad$ (c) 850$\quad$ (d) 800
View full solution →(i) What is the total number of persons living in the town in the age-groups 10-15 and 60 - 65?
(a) 2000$\quad$ (b) 2200$\quad$ (c) 2100$\quad$ (d) 1900
(ii) How many persons are more in the age-group 10 - 15 than in the age group 30-35?
(a) 200$\quad$ (b) 250$\quad$ (c) 300$\quad$ (d) 350
(iii) What is the total population of the town?
(a) 6700$\quad$ (b) 6400$\quad$ (c) 7700$\quad$ (d) 6600
(iv) What is the number of persons in the age-group 60-65?
(a) 900$\quad$ (b) 750$\quad$ (c) 850$\quad$ (d) 800
Following bar graph represents the sales of cold drinks of two companies A and B from 2015 to 2018.
Read the above bar graph and answer the following questions:
(i) The year in which the difference between the sales of two companies was highest, was
(a) 2018$\quad$ (b) 2015$\quad$ (c) 2016$\quad$ (d) 2017$\quad$
(ii) Total sales of A and B in the year 2016 was
(a) 1,160,000 units$\quad$ (b) 1,270,000 units$\quad$ (c) 1,380,000 units$\quad$ (d) 1,490,000 units
(iii) The minimum difference between the sales of company A and B in any year in the given period was
(a) 90,000 units$\quad$ (b) 70,000 units$\quad$ (c) 50,000 units$\quad$ (d) 30,000 units
(iv) In which year was the sales of company B more than the sales of company A?
(a) 2015$\quad$ (b) 2016$\quad$ (c) 2017$\quad$ d) 2018
(v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107:145$\quad$ (b) 29:36$\quad$ (c) 127: 145$\quad$ (d) 107: 127
View full solution →Read the above bar graph and answer the following questions:
(i) The year in which the difference between the sales of two companies was highest, was
(a) 2018$\quad$ (b) 2015$\quad$ (c) 2016$\quad$ (d) 2017$\quad$
(ii) Total sales of A and B in the year 2016 was
(a) 1,160,000 units$\quad$ (b) 1,270,000 units$\quad$ (c) 1,380,000 units$\quad$ (d) 1,490,000 units
(iii) The minimum difference between the sales of company A and B in any year in the given period was
(a) 90,000 units$\quad$ (b) 70,000 units$\quad$ (c) 50,000 units$\quad$ (d) 30,000 units
(iv) In which year was the sales of company B more than the sales of company A?
(a) 2015$\quad$ (b) 2016$\quad$ (c) 2017$\quad$ d) 2018
(v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107:145$\quad$ (b) 29:36$\quad$ (c) 127: 145$\quad$ (d) 107: 127
A healthcare survey was done by the State Health and Family Welfare Care Board of the State of Punjab. The data is collected by forming age groups i.e. 10-15, 20-25, 30-35, 40-45, 50-55, 60-65, 70-75. The overall data from a town is given below in the form of a bar graph. Read the data carefully and answer the question that follow:
(i)How many persons are more in the age group 10 - 15 than in the age group 30 - 35?
(ii)What is the age group of exactly 1200 persons living in the town?
(iii)What is the percentage of the youngest age group persons over those in the oldest age group?
(iv) What is the total population of the town?
(i)How many persons are more in the age group 10 - 15 than in the age group 30 - 35?
(ii)What is the age group of exactly 1200 persons living in the town?
(iii)What is the percentage of the youngest age group persons over those in the oldest age group?
(iv) What is the total population of the town?
The population of Delhi State in different census years is as given below:
Represent the above information with the help of a bar graph.
| Census year | 1961 | 1971 | 1981 | 1991 | 2001 |
| Population in Lakhs | 30 | 55 | 70 | 110 | 150 |
The investments (in ten crores of rupees) of Life Insurance Corporation of India in different sectors is given below:
Represent the above data with the help of a bar graph.
| Sectors | Investment (in ten crores of rupess) |
| Central government securities | 45 |
| State government securities | 11 |
| Securities guaranteed by the government | 23 |
| Private sectors | 18 |
| Socially oriented sectors (plan) | 46 |
| Socially oriented sectors (Non–plan) | 11 |
The following table gives the quantity of goods (in crores of rupees)
Represent this information with the help of a bar graph.
| Year | 1950–51 | 1960–61 | 1965–66 | 1970–71 | 1980–81 | 1982–83 |
| Quantity of goods (in crore tonnes) | 9 | 16 | 20 | 20 | 22 | 26 |
The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:
Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.
| Years | 1982–83 | 1983–84 | 1984–85 | 1985–86 | 1986–87 |
| Value of exports of cotton textiles (in crores of rupees) | 300 | 325 | 475 | 450 | 550 |
The following data gives the demand estimates of the Government of India, Department of Electronics for the personnel in the Computer sector during the Eighth Plan period (1990–95):
Represent the data with the help of a bar graph. Indicate with the help of the bar graph the course where the estimated requirement is least.
| Qualifications | MCA (Masters in Computer Applications) | DCA (Diploma in Computer Applications | DCE (Diploma in Computer Engineering) | CL (Certificate Level Course) | ST (Short Term Course) |
| Personnel required | 40600 | 181600 | 18600 | 670600 | 1802900 |
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