The word statistics is used for two different meanings.
In the singular sense, it is used as a science or a subject which deals with the collection,
classification, tabulation, representation and interpretation of the data.
In the plural sense, it is sometimes used for the numerical facts collected in the form of
If we have collected information about the heights of class 6 children from ten different
schools of Delhi, then this information in the form of numbers is called statistics.
1. Data : Each number, collected for giving a required information, is called the data.
2. Bar Graph (Column Graph) : Bar graph is the simplest form of presenting a data. It
consists of bars (usually vertical), all of same widths. The heights of these bars are
drawn according to the number they represent.
3. Pie Graph : When the given data is represented by the sectors of a circle, the
resulting diagram (graph) obtained is called a pie-graph or a pie-chart.
EXERCISE 33 (A)
Marks scored by 30 students of class VI are as given below :
38, 46, 33, 45, 63, 53, 40, 85, 52, 75, 60, 73, 62, 22, 69, 43, 45, 33, 47, 41, 29, 43, 37,
49, 83, 44, 55, 22, 35 and 45. State:
(i) the highest marks scored.
(ii) the lowest marks scored.
(iii) the range of marks.
(i) Highest marks scored = 85 .
(ii) Lowest marks scored = 22
(iii) Range of marks = 85
– 22 = 63
For the following raw data, form a discrete frequency distribution :
30,32,32, 28,34,34,32,30,30,32,32,34,30,32,32. 28,32,30, 28,30,32,32,30,28 and 30.
(ii) frequency of an observation.
(i) Data : The word data means information in the form of numerical figures.
(ii) Frequency of an observation : The number of times a particular observation
occurs is called its frequency.
Rearrange the following raw data in descending order :
5.3, 5.2, 5.1, 5.7, 5.6, 6.0, 5.5, 5.9, 5.8, 6.1, 5.5, 5.8, 5.7, 5.9 and 5.4. Then write the :
(i) highest value
(ii) lowest value
(iii) range of values
Writing these numbers in descending order we get:
6.1, 6.0, 5.9, 5.9, 5.8, 5.8, 5.7, 5.7, 5.6, 5.5, 5.5, 5.4, 5.3, 5.2, 5.1
(i) Highest value = 6.1
(ii) Lowest value = 5.1
(iii) Range of values = Highest value
– lowest value = 6.1 -5.1 = 1.0
Represent the following data in the form of a frequency distribution :
52, 56, 72, 68, 52, 68, 52, 68, 52, 60, 56, 72, 56, 60, 64, 56, 48, 48, 64 and 64.
In a study of number of accidents per day, the observations for 30 days were
obtained as follows :
The required frequency table will be as shown below :
The following data represents the w
eekly wages (in ₹) of 15 workers in a factory :
900, 850, 800, 850, 800, 750, 950, 900, 950, 800, 750, 900, 750, 800 and 850.
Prepare a frequency distribution table. Now find,
(i) how many workers are getting less than ₹850 per week?
(ii) how many workers
are getting more than ₹800 per week?
Workers getting less than ₹850 per week
No. of workers getting ₹750 = 3 workers
No. of workers getting ₹800 = 4 works
∴ Workers getting less than ₹ 850 = 4 + 3 = 7 workers
Workers are getting more than ₹800 per week
No. of workers getting ₹850 = 3
No. of workers getting ₹900 = 3
No. of workers getting ₹950 = 2
∴Workers getting more than ₹800 = 3 + 3 + 2 = 8 workers
Using the data, given below, construct a frequency distribution table : 9, 17, 12,
20, 9, 18, 25, 17, 19, 9, 12, 9, 12, 18, 17, 19, 20, 25, 9 and 12. Now answer the
(i) How many numbers are less than 19?
(ii) How many numbers are more than 20?
(iii) Which of the numbers, given above, is occuring most frequently?
The required frequency table will be as shown below :
(i) There are 14 numbers are less than 19.
(ii) There are 2 numbers more than 20.
(iii) 9 is occuring most frequently i.e. 5 times.
Using the following data, construct a frequency distribution table : 46, 44, 42, 54,
52, 60, 50, 58, 56, 62, 50, 56, 54, 58 and 48.
Now answer the following :
(i) What is the range of the numbers?
(ii) How many numbers are greater than 50?
(iii) How many numbers are between 40 and 50?
(i) Range of numbers = Highest number
– Lowest number = 62 – 42 = 20
(ii) 9 numbers are greater than 50
(iii) 6 numbers are between 40 and 50 Ans.
EXERCISE 33 (B)
The sale of vehicles, in a particular city, during the first six months of the year
2016 is shown below :
Draw a pictograph to represent the above data.
(i) Cars sold by dealer A = 6 x 50 = 300
Cars sold by dealer D = 4 x 5 = 200 ,
∴ A sold more cars than dealer D by = 300 – 200 = 100
∴A has sold 100 more cars than dealer D.
(ii) No. of cars = 23
Scale = 50 cars
∴Total no. of cars = 23 x 50 = 1150 cars Ans.
The following pictograph shows the number of watches manufactured by a
factory, in a particular weeks.
(i) on which day were the least number of watches manufactured ?
(ii) total number of watches manufactured in the whole week ?
(i) On Friday least no. of watches manufactured by = 100 x 5 = 500 watches
(ii) Total no. of watches manufactured in the whole week = 100 x 42.5 = 4250 watches
The number or animals in five villages are as follows :
Prepare a pictograph of these animals using one symbol to represent 20 animals.
The following pictograph shows different subject books which are kept in a
Taking symbol of one book = 50 books, find :
(i) how many History books are there in the library ?
(ii) how many Science books are there in the library ?
(iii) which books are maximum in number ?
(i) There are 50 x 4 = 200 History books in the library.
(ii) There are 50 x 5.5 = 275 Science books in the library.
(iii) English books are maximum in number = 500 x 9 = 450 books.
EXERCISE 33 (C)
The following table gives the number of students in class VI in a school during
academic years 2011-2012 to 2015-2016.
Represent the above data by a bar graph.
The attendance of a particular class for the six days of a week are as given below
Draw a suitable graph.
The total number of students present in class VI B, for the six days in a week
were as given below. Draw a suitable bar graph.
The following table shows the population of a particular city at different years :
Represent the above information with the help of a suitable bar graph.
In a survey of 300 families of a colony, the number of children in each family was
recorded and the data has been represented by the bar graph, given below :
Read the graph carefully and answer the following questions :
(i) How many families have 2 children each ?
(ii) How many families have no child ?
(iii) What percentage of families have 4 children ?
(i) 60 families have 2 children each.
(iii) The percentage of families having 4 children =
x 100 = 20%
Use the data, given in the following table, to draw’ a bar graph
Out of A, B, C, D, E and F
(i) Which has the maximum value.
(ii) Which is greater A + D or B + E.
(i) D has the maximum value of 350
(ii) A + D = 250 + 350 = 600
B + E = 300 + 275 = 575
Hence A + D is greater.
The bar graph drawn below shows the number of tickets sold during a fair by 6
students A, B, C, D, E and F.
Using the Bar graph, answer the following questions :
(i) Who sold the least number of tickets?
(ii) Who sold the maximum number of tickets ?
(iii) How many tickets were sold by A, B and C taken together ?
(iv) How many tickets were sold by D, E and F taken together ?
(v) What is the average number of tickets sold per student ?
The following bar graph shows the number of children, in various classes, in a
school in Delhi.
Using the given bar graph, find :
(i) the number of children in each class.
(ii) the total number of children from Class 6 to Class 8.
(iii) how many more children there are in Class 5 compared to Class 6 ?
(iv) the total number of children from Class 1 to Class 8.
(v) the average number of children in a class.
(i) In, Class 1 = 100, Class 2 = 90, Class 3 = 100, Class 4 = 80,
Class 5 = 120, Class 6 = 90, Class 7 = 70, Class 8 = 50
(ii) Class 6 = 90, Class 7 = 70, Class 8 = 50, Total number = 210
(iii) Number of student in class 5 = 120, Number of student in class 6 = 90
More children is class 5 = (120
– 90) = 30
(iv) Total number of children class 1 to 8 = 100 + 90+ 100+ 80 + 120 +90 + 70 + 50 =
The column graph, given above , shows the number of patients, examined by Dr.
V.K. Bansal, on different days of a particular week.
Use the graph to answer the following:
(i) On which day were the maximum number of patients examined ?
(ii) On which day were the least number of patients examined ?
(iii) On which days were equal number or patients examined ?
(iv) What is the total number of patients examined in the week ?
(i) Tuesday were the maximum number of patients examined.
(ii) Friday were the least number of patients examined.
(iii) Sunday and Thursday were equal number of patient examined.
(iv) Total number of patients examined in the week .
= 50 + 40 + 70 + 60 + 50 + 30 = 300
A student spends his pocket money on various items, as given below :
Books : Rs. 380, Postage : Rs. 30, Cosmetics : Rs. 240, Stationary : Rs. 220 and
Entertainment : Rs. 120.
Draw a bar graph to represent his expenses.
Amount spent on
Books = Rs. 380
Postage = Rs. 30
Cosmetics = Rs. 240
Stationary = Rs. 220
Entertainment = Rs. 120