Information collected in the form of numbers is called data. In this chapter, we arrange data in a frequency table using tally marks. We also read and draw bar graphs with a proper scale. We learn to show information with pictures, called an infographic.
Key points
For every score, we draw one tally mark. The fifth tally mark is drawn across the first four.
The number of times a score appears is its frequency.
The total of all frequencies is written as N.
In a bar graph, all the bars have the same width. The gap between two bars is also the same.
Choose a suitable scale on the Y-axis before drawing a bar graph.
Formulas and terms
Score – each item or number in the data.
Frequency – the number of times a score occurs.
Bar graph – data shown by bars of different heights.
Infographic – data shown with pictures or symbols.
Practice Set 18.1
1The number of saplings planted by 30 students of the Green Army in a school is given in the frequency table below. Complete the following table.
Number of saplings
Tally Marks
Frequency
1
||||
4
2
ᐱ |
6
3
ᐱ ᐱ ||
12
4
ᐱ |||
8
Total
N = 30
2The number of buffaloes owned by 40 families in the village Vani is as follows. 1, 6, 5, 4, 3, 2, 7, 2, 3, 4, 6, 5, 3, 2, 6, 4, 5, 5, 3, 2, 3, 4, 2, 5, 4, 3, 7, 6, 5, 4, 1, 2, 3, 2, 6, 4, 6, 5, 4, 2. Prepare a frequency table from this data.
Number of buffaloes (Score)
Tally Marks
Number of families (Frequency)
1
||
2
2
ᐱ |||
8
3
ᐱ ||
7
4
ᐱ |||
8
5
ᐱ ||
7
6
ᐱ |
6
7
||
2
Total
N = 40
Check: 2 + 8 + 7 + 8 + 7 + 6 + 2 = 40 families.
3Given a number below, prepare a frequency table of the digits after the decimal point. 3.14159265358979323846264338327950288419716939937517
Only the 50 digits after the decimal point are counted.
4Shailaja gave the following names to the birds in the forest for her survey: M-Peacock, S-Stork, K-Cuckoo, W-Woodpecker, G-Eagle. Prepare a frequency table of birds in the forest based on her survey.
Bird
Tally Marks
Frequency
M — Peacock
ᐱ |||
8
S — Stork
ᐱ ᐱ ᐱ ᐱ ᐱ |
26
K — Cuckoo
||||
4
W — Woodpecker
||||
4
G — Eagle
ᐱ ||||
9
Total
N = 51
Check: 8 + 26 + 4 + 4 + 9 = 51 birds recorded.
Count the letters in your textbook carefully once again. Draw one tally mark for each letter.
Practice Set 18.2
1The following bar graph shows the information about the plants in the nursery. Observe the graph and answer the questions.
The bar graph given in the question.
i) What information is shown on the X and Y axes?
The X-axis shows the types of plants in the nursery. The Y-axis shows the number of plants of each type.
ii) What kind of flower plants are there in the nursery?
There are Jasmine, Jai, Hibiscus and Chrysanthemum plants in the nursery.
iii) Which plant has the highest number?
Chrysanthemum plants are the highest in number (80).
iv) How many more are the number of chrysanthemum plants than Jasmine plants?
Chrysanthemum = 80, Jasmine = 70 80 − 70 = 10
There are 10 more chrysanthemum plants.
v) What is the total number of plants in the bar graph?
70 + 50 + 40 + 80 = 240
There are 240 plants in all.
2The average estimated lifespan of some animals is given below. Draw a bar graph showing this information with appropriate scale. Ox 28 years, Horse 30 years, Dog 22 years, Cat 25 years, Goat 15 years, Cow 22 years.
Scale: On the Y-axis, 1 cm = 5 years.
Bar graph of the average estimated lifespan of the six animals.
3The table below shows the monthly expenditure of John's family on various items. (Scale: On the Y axis take 1 cm = ₹500). Draw a bar graph according to the given scale.
Bar graph of the family's monthly expenditure, drawn to the given scale.
4The number of students participating in variety entertainment programmes in a school's gathering is shown in the table below. Draw a bar graph based on this information.
Scale: On the Y-axis, 1 cm = 4 students.
Bar graph of the number of students in each programme.
Total students taking part = 24 + 40 + 16 + 8 + 4 = 92
5A survey was conducted on students in a village about what they would like to do in their free time. Draw a bar graph based on this information.
Scale: On the Y-axis, 1 cm = 5 students.
Bar graph of the free-time survey.
Exercise 18
1The travel time from Pune to Mumbai by different modes of transport is as follows: car 4, bus 5, Railway 3, Airplane 1 (hours). Draw a bar graph based on the above information.
Scale: On the Y-axis, 1 cm = 1 hour.
Bar graph of the travel time by each mode of transport.
2The time (in minutes) allotted for daily exercise by 20 people in an ashram is given. 25, 30, 40, 20, 15, 35, 45, 50, 25, 30, 60, 55, 20, 15, 40, 35, 50, 45, 30, 25. Prepare a frequency table based on the above information.
3A question was asked to 30 students in a class, "In what way do you like to learn science?" Draw a bar graph based on the given information.
Bar graph of the 30 students’ preferred way of learning science.
Check: 10 + 7 + 5 + 4 + 4 = 30 students.
4The frequency table of prime numbers between 1 and 50 is given below. Complete the table.
The prime numbers between 1 and 50 are:
1 to 10 – 2, 3, 5, 7 – 4 primes
11 to 20 – 11, 13, 17, 19 – 4 primes
21 to 30 – 23, 29 – 2 primes
31 to 40 – 31, 37 – 2 primes
41 to 50 – 41, 43, 47 – 3 primes
Score
Tally marks
Frequency
1 to 10
||||
4
11 to 20
||||
4
21 to 30
||
2
31 to 40
||
2
41 to 50
|||
3
Total
N = 15
5Information about the hobbies of each of the 25 senior citizens in a society was collected. Based on the information, prepare a frequency table and draw a bar graph of that information.
The frequency table
Hobby
Tally Marks
Number of senior citizens
Singing
ᐱ
5
Sports
ᐱ ᐱ |
11
Drawing
||||
4
Reading
ᐱ
5
Total
N = 25
Check: 5 + 11 + 4 + 5 = 25 senior citizens.
The bar graph
Bar graph drawn from the frequency table above.
6Pooja, Umesh, Pradeep, Madhuri have 3, 1, 4, 5 postage stamps respectively. Draw an infographic of this information.
In an infographic, information is shown with pictures. Here, one stamp picture stands for one postage stamp.
An infographic using one stamp symbol for each stamp collected.
