R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 16  Presentation of Data in Tabular Form
Chapter 16  Presentation of Data in Tabular Form Exercise Ex. 16
Define statistics as a subject.
Statistics is a branch of science which deals with the collection, presentation, analysis and interpretation of numerical data.
Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 912, where 12 is not included.
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17, 15, 6, 18, 23, 22, 16, 9, 21, 11, 16.
Grouped Frequency Distribution Table:
Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210230 (230 not included).
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.
Minimum observation is 210 and maximum observation =320
So the range is (320210)=110
The classes of equal size covering the given data are :
(210230), (230250), (250270) , (270290), (290310), (310330)
Thus the frequency distribution may be given as under :
The weights (in grams ) of 40 oranges picked at random from a basket are as follow :
40, 50, 60, 65, 45, 55, 30, 90, 75, 85, 70,85, 75, 80, 100, 110, 70, 55, 30, 35, 45, 70, 80, 85, 95, 70, 60, 70, 75, 40, 100, 65, 60, 40, 100, 75, 110, 30, 45, 84.
Construct a frequency table as well as a cumulative frequency table.
Minimum observation is 30 and maximum observation is 110
So, range is 10030=80
The classes of equal size covering the given data are :
(3040) ,(4050) , (5060) ,(6070) , (7080), (8090),(90100),(100110), (110120)
Thus , the frequency and cumulative frequency table may be given as under :
The heights (in cm) of 30 students of a class are given below:
161, 155, 159, 153, 150, 158, 154, 158, 160, 148, 149, 162, 163, 159, 148, 153, 157, 151, 154, 157, 153, 156, 152, 156, 160, 152, 147, 155, 155, 157.
Prepare a frequency table as well as a cumulative frequency table with 160165 (165 not included) as one of the class intervals.
Grouped Frequency Distribution Table and Cumulative Frequency Table:
Following are the ages (in years ) of 360 patients , getting medical treatment in a hospital:
Age (in years) 
1020 
2030 
3040 
4050 
5060 
6070 
Number of patients 
90 
50 
60 
80 
50 
30 
Construct the cumulative frequency table for the above data.
Age (in years) (age) 
No of patients (Frequency) 
Cumulative Frequency 
1020 2030 3040 4050 5060 6070 
90 50 60 80 50 30 
90 140 200 280 330 360 
Total 
360 

Present the following as an ordinary grouped frequency table :
Marks(below) 
10 
20 
30 
40 
50 
60 
Number of students 
5 
12 
32 
40 
45 
48 
Marks (below) 
No of students(Cumulative Frequency.) 
Class Intervals 
Frequency 
10 20 30 40 50 60

5 12 32 40 45 48

010 1020 2030 3040 4050 5060

5 12  5 = 7 32  12 = 20 40  32 = 8 45  40 = 5 48  45 = 3 


Total 
48

Given below is a cumulative frequency table ;
Marks 
Number of students 
Below 10 
17 
Below 20

22 
Below 30 
29 
Below 40 
37 
Below 50 
50 
Below 60 
60 
Extract a frequency table from the above .
Marks (below) 
No of students(Cumulative Frequency) 
Class Intervals 
Frequency 
10 20 30 40 50 60

17 22 29 37 50 60 
010 1020 2030 3040 4050 5060

17 22  17 = 5 29  22 = 7 37  29 = 8 50  37 = 13 60  50 = 10 


Total 
60

Make a frequency table from the following ;
Marks obtained 
Number of students 
More than 60 
0 
More than50 
16 
More than40 
40 
More than30 
75 
More than20 
87 
More than10 
92 
More than0 
100 
Marks (below) 
No of student s(C.F.) 
Class Intervals 
Frequency 
More than 60 More than 50 More than 40 More than 30 More than 20 More than 10 More than 0

0 16 40 75 87 92 100 
More than 60 5060 4050 3040 2030 1020 010 
0 160=16 4016=24 7540=35 8775=12 9287=5 10092=8



Total 
100

The marks obtained by 17 students in a mathematics test (out of 100) are given below:
90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68.
Find the range of the above data.
Arranging data in ascending order, we have
46, 48, 49, 64, 65, 66, 68, 72, 76, 79, 82, 82, 90, 91, 96, 100, 100
Minimum marks = 46
Maximum Marks = 100
∴ Range of the above data = Maximum Marks  Minimum Marks
= 100  46
= 54
(i) Find the class mark of the class 90  120.
(ii) In a frequency distribution, the midvalue of the class is 10 and width of the class is 6. Find the lower limit of the class.
(iii) The width of each of five continuous classes in a frequency distribution is 5 and lower class limit of the lowest class is 10. What is the upper class limit of the highest class?
(iv) The class marks of a frequency distribution are 15, 20, 25, ... Find the class corresponding to the class mark 20.
(v) In the class intervals 1020, 2030, find the class in which 20 is included.
Define some fundamental characteristics of statistics.
Fundamental characteristics of statistics :
(i) It deals only with the numerical data.
(ii) Qualitative characteristic such as illiteracy, intelligence, poverty etc cannot be measured numerically
(iii) Statistical inferences are not exact.
Find the values of a, b, c, d, e, f, g from the following frequency distribution of the heights of 50 students in a class:
Height (in cm) 
Frequency 
Cumulative frequency 
160165 
15 
a 
165170 
b 
35 
170175 
12 
c 
175180 
d 
50 
180185 
e 
55 
185190 
5 
f 

g 

Height (in cm) 
Frequency 
Cumulative frequency 
160165 
15 
a = 15 
165170 
b = 35  15 = 20 
35 
170175 
12 
c = 35 + 12 = 47 
175180 
d = 50  47 = 3 
50 
180185 
e = 55  50 = 5 
55 
185190 
5 
f = 55 + 5 = 60 

g = 60 

What are the primary data and secondary data? Which of the two is more reliable and why?
Primary data: Primary data is the data collected by the investigator himself with a definite plan in his mind. These data are very accurate and reliable as these being collected by the investigator himself.
Secondary Data: Secondary data is the data collected by a person other than the investigator.
Secondary Data is not very reliable as these are collected by others with purpose other than the investigator and may not be fully relevant to the investigation.
Explain the meaning of each of the following terms.
(i)Variate(ii) Class interval(iii)Class size
(iv)Class mark (v)Class limit(vi)True class limits
(vii)Frequency of a class(viii) Cumulative frequency of a class
(i)Variate : Any character which can assume many different values is called a variate.
(ii)Class Interval :Each group or class in which data is condensed is calleda class interval.
(iii)ClassSize :The difference between the true upper limitand the true lower limit of a class is called class size.
(iv)Classmark : The average of upper and lower limit of a class interval is called its class mark.
i.e Class mark=_{}
(v) Class limit: Class limits are the two figures by which a class is bounded . The figure on the left side of a class is called lower lower limit and on the right side is called itsupper limit.
(vi)True class limits: In the case of exclusive form of frequency distribution, the upper class limits and lower classlimits are the true upper limits and thetrue lower limits. But in the case of inclusive form of frequency distribution , the true lower limit of a class is obtained by subtracting 0.5 from the lower limit of the class. And the true upper limit of the class is obtained by adding 0.5 to the upper limit.
(vii)Frequency of a class : The number of observations falling in aclass determines its frequency.
(viii)Cumulative frequency of a class: The sum of all frequenciesup to and including that class is called , the cumulative frequency of that class.
The blood groups of 30 students of a class are recorded as under:
A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
(i) Represent this data in the form of a frequency distribution table.
(ii) Find out which is the most common and which is the rarest blood group among these students.
(i) Frequency Distribution Table:
(ii) The most common blood group is 'O' and the rarest blood group is 'AB'.
Three coins are tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 1, 3, 2, 0, 2.
Prepare a frequency distribution table.
Frequency Distribution Table:
Following data gives the number of children in 40 families :
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1,2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent in the form of a frequency distribution, taking classes 02, 24, etc.
Thus , the frequency distribution may be given as under:
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as under:
8, 4, 8, 5, 1, 6, 2, 5, 3, 12, 3, 10, 4, 12, 2, 8, 15, 1, 6, 17, 5, 8, 2, 3, 9, 6, 7, 8, 14, 12.
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class interval as 5  10.
(ii) How many children watched television for 15 or more hours a week?
(i) Grouped Frequency Distribution Table:
(ii) 2 children watch television for 15 or more hours a week.
The marks obtained by 40 students of a class in an examination are given below .
3, 20, 13, 1, 21, 13, 3, 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 24, 6, 23, 15.
Present the data in the form of a frequency distribution using equal class size, one such class being 1015(15 not included).
Minimum observation is 1 and minimum observation is 24. The classes of equal size converging the given data are : (05), (510), (1015), (1520), (2025)
Thus, the frequency distribution may be given as under :
Chapter 16  Presentation of Data in Tabular Form Exercise MCQ
The range of the data
12,25,15,18,17,20,22,6,16,11,8,19,10,30,20,32 is
 10
 15
 18
 26
Correct option: (d)
Range = maximum value  minimum value
= 32  6
= 26
The class mark of the class 100120 is
 100
 110
 115
 120
In the class intervals 1020, 2030, the number 20 is included in
 1020
 2030
 In each of 1020 and 2030
 In none of 1020 and 2030
The class marks of a frequency distribution are 15, 20, 25, 30………. The class corresponding to the mark 20 is
 12.517.5
 17.522.5
 18.521.5
 19.520.5
In a frequency distribution, the midvalue of a class is 10 and width of each class is 6. The lower limit of the class is
 6
 7
 8
 12
The mid  value of a class interval is 42 and the class size is 10. The lower and upper limits are
 3747
 37.547.5
 36.547.5
 36.546.5
Let m be in the midpoint and u be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is
 2m  u
 2m + u
 m  u
 m + u
The width of each of the five continuous classes in a frequency distribution is 5 and the lower class limit of the class is
 45
 25
 35
 40
Let L be the lower class boundary of a class in a frequency distribution and m be the midpoint of the class. Which one of the following is the upper class boundary of the class?
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