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Practice each question, then open the answer or worked solution.
Draw a histogram for the following data.
| Class interval | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
| Frequency | 30 | 98 | 80 | 58 | 29 | 50 |
Solution:-
Scale:
On X – axis, 1 big division = 5 marks
On Y – axis, 1 big division = 10 students
In a hypothetical sample of 20 people, the amount of money (in thousands of rupees) with each was found to be as follows:
114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118.
Draw a histogram of the frequency distribution, taking one of the class intervals as
50 –100.
Solution:-
From the data given in the question, first, we have to prepare a frequency distribution table,
Scale:
On X – axis, 1 big division = 50 ₹ marks
On Y – axis, 1 big division = 2 persons
The below histogram shows the number of literate females in the age group of 10 to 40 years in a town.
(a) Write the classes assuming all the classes are of equal width.
(b) What is the class’s width?
(c) In which age group are literate females the least?
(d) In which age group is the number of literate females the highest?
Solution:-
(a) The classes are, 10-15, 15-20, 20-25, 25-30, 30-35, and 35-40
b) The class width is 15 – 10 = 5
c) In the class first group i.e. 10-15 have the least female literate.
d) In the class second group i.e. 15-20 have the highest female literate.
The following histogram shows the frequency distribution of teaching experiences of 30 teachers in various schools:
(a) What is the class width?
Solution:-
The width of the class is 5.
(b) How many teachers have the maximum teaching experience, and how many have the least teaching experience?
Solution:-
Teachers having maximum teaching experience is 2, and Teachers having least teaching experience is 5.
(c) How many teachers have teaching experience of 10 to 20 years?
Solution:-
Teachers have teaching experience of 10 to 20 years is 7 + 2 = 9.
In a district, the number of branches of different banks is given below:
| Bank | State Bank of India | Bank of Baroda | Punjab National Bank | Canara Bank |
| Number of Branches | 30 | 17 | 15 | 10 |
Draw a pie chart for this data.
Solution:-
From the table,
Total number of branches of different banks in a district = 30 + 17 + 15 + 10
= 72
Central angle of pie chart for each bank,
State Bank of India = (30/72) × 360o
= 150o
Bank of Baroda = (17/72) × 360o
= 85o
Punjab National bank = (15/72) × 360o
= 75o
Canara Bank = (10/72) × 360o
= 50o
For the development of basic infrastructure in a district, a project of Rs 108 crore approved by the Development Bank is as follows:
| Item Head | Road | Electricity | Drinking water | Sewerage |
| Amount in crore (Rs) | 43.2 | 16.2 | 27.00 | 21.6 |
Draw a pie chart for this data.
Solution:-
From the question,
Total number approved = 108 crore
Central angle of pie chart for each infrastructure,
Road = (43.2/108) × 360o
= 144o
Electricity = (16.2/108) × 360o
= 54o
Drinking water = (27/108) × 360o
= 90o
Sewerage = (21.6/108) × 360o
= 72o
In the time table of a school, periods allotted per week to different teaching subjects are given below:
| Subject | Hindi | English | Maths | Science | Social Science | Computer | Sanskrit |
| Periods Allotted | 7 | 8 | 8 | 8 | 7 | 4 | 3 |
Draw a pie chart for this data.
Solution:-
From the question,
Total number periods allotted = 7 + 8 + 8 + 8 + 7 + 4 + 3 = 45 periods
Central angle of pie chart for each subject,
Hindi = (7/45) × 360o
= 56o
English = (8/45) × 360o
= 64o
Maths = (8/45) × 360o
= 64o
Science = (8/45) × 360o
= 64o
Social Science = (7/45) × 360o
= 56o
Computer = (4/45) × 360o
= 32o
Sanskrit = (3/45) × 360o
= 24o
A survey was carried out to find the favourite beverage preferred by a certain group of young people. The following pie chart shows the findings of this survey. From this pie chart, answer the following:
(i) Which type of beverage is liked by the maximum number of people?
Solution:-
Cold drink is liked by the maximum number of people.
(ii) If 45 people like tea, how many people were surveyed?
Solution:-
From the question, it is given that,
45 people like tea
Then,
Let us assume the total number of people surveyed be x,
= 45 = (15/100) × (x)
= 45 = 0.15x
= x = 45/0.15
= x = 300
So, the total number of people surveyed is 300.
The following data represents the approximate percentage of water in various oceans. Prepare a pie chart for the given data.
Pacific 40%
Atlantic 30%
Indian 20%
Others 10%
Solution:-
The central angle of the given approximate percentage of water in various oceans,
Pacific = (40/100) × 360o
= 144o
Atlantic = (30/100) × 360o
= 108o
Indian = (20/100) × 360o
= 72o
Others = (10/100) × 360o
= 36o
At a Birthday Party, the children spin a wheel to get a gift. Find the probability of
(a) getting a ball
Solution:-
Number of balls in wheel = 2
Total number of gifts = 8
Probability of getting a ball = Number of balls in wheel/ total number of gifts
= 2/8 … [divide both by 2]
= 1/4
(b) getting a toy car
Solution:-
Number of cars in wheel = 3
Total number of gifts = 8
Probability of getting a ball = Number of balls in wheel/total number of gifts
= 3/8
(c) any toy except a chocolate
Solution:-
Number of toys except a chocolate = 7
Total number of gifts = 8
Probability of getting a ball = Number of balls in wheel/total number of gifts
= 7/8