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RS Aggarwal Solutions Class 9 Maths Chapter 16 Presentation of Data in Tabular Form

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Question 1

Define statistics as a subject.

Solution 1

Statistics is a branch of science which deals with the collection, presentation, analysis and interpretation of numerical data.

Question 2

Define some fundamental characteristics of statistics.

Solution 2

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.

Question 3

What are the primary data and secondary data? Which of the two is more reliable and why?

Solution 3

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.

Question 4

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

Solution 4

(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)Class-Size :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.

Question 5

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.

Solution 5

(i) Frequency Distribution Table:

(ii) The most common blood group is ‘O’ and the rarest blood group is ‘AB’.

Question 6

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.

Solution 6

Frequency Distribution Table:

Question 7

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 0-2, 2-4, etc.

Solution 7

nimum observation is 0 and maximum observation is 6. The classes of equal size covering the given data are : (0-2), (2-4), (4-6) and (6-8).

Thus , the frequency distribution may be given as under:

Question 8

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?

Solution 8

(i) Grouped Frequency Distribution Table:

(ii) 2 children watch television for 15 or more hours a week.

Question 9

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 10-15(15 not included).

Solution 9

Minimum observation is 1 and minimum observation is 24. The classes of equal size converging the given data are : (0-5), (5-10), (10-15), (15-20), (20-25)

Thus, the frequency distribution may be given as under :

Question 10

Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, 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.

Solution 10

Grouped Frequency Distribution Table:

Question 11

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 210-230 (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.

Solution 11

Minimum observation is 210 and maximum observation =320

So the range is (320-210)=110

The classes of equal size covering the given data are :

(210-230), (230-250), (250-270) , (270-290), (290-310), (310-330)

Thus the frequency distribution may be given as under :

Question 12

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.

Solution 12

Minimum observation is 30 and maximum observation is 110

So, range is 100-30=80

The classes of equal size covering the given data are :

(30-40) ,(40-50) , (50-60) ,(60-70) , (70-80), (80-90),(90-100),(100-110), (110-120)

Thus , the frequency and cumulative frequency table may be given as under :

Question 13

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 160-165 (165 not included) as one of the class intervals.

Solution 13

Grouped Frequency Distribution Table and Cumulative Frequency Table:

Question 14

Following are the ages (in years ) of 360 patients , getting medical treatment in a hospital:

Age (in years) |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |

Number of patients |
90 |
50 |
60 |
80 |
50 |
30 |

Construct the cumulative frequency table for the above data.

Solution 14

Age (in years) (age) |
No of patients (Frequency) |
Cumulative Frequency |

10-20 20-30 30-40 40-50 50-60 60-70 |
90 50 60 80 50 30 |
90 140 200 280 330 360 |

Total |
360 |

Question 15

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 |
0-10 10-20 20-30 30-40 40-50 50-60 |
5 12 – 5 = 7 32 – 12 = 20 40 – 32 = 8 45 – 40 = 5 48 – 45 = 3 |

Total |
48 |

Question 16

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 .

Solution 16

Marks (below) |
No of students(Cumulative Frequency) |
Class Intervals |
Frequency |

10 20 30 40 50 60 |
17 22 29 37 50 60 |
0-10 10-20 20-30 30-40 40-50 50-60 |
17 22 – 17 = 5 29 – 22 = 7 37 – 29 = 8 50 – 37 = 13 60 – 50 = 10 |

Total |
60 |

Question 17

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 |

Solution 17

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 50-60 40-50 30-40 20-30 10-20 0-10 |
0 16-0=16 40-16=24 75-40=35 87-75=12 92-87=5 100-92=8 |

Total |
100 |

Question 18

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.

Solution 18

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

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