Frequency Distribution Class 9 RS Aggarwal Exe-15 Goyal Brothers ICSE Maths Solutions Ch-15. In this article you will learn Frequency Distribution problems easily. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.
Frequency Distribution Class 9 RS Aggarwal Exe-15 Goyal Brothers ICSE Maths Solutions Ch-15
| Board | ICSE |
| Subject | Maths |
| Class | 9th |
| Chapter-15 | Frequency Distribution |
| Writer | RS Aggrawal |
| Topics | Solved Practice Questions |
| Academic Session | 2024-2025 |
Frequency Distribution
A frequency distribution is a representation, either in a graphical or tabular format, that displays the number of observations within a given interval
Exercise- 15
(Frequency Distribution Class 9 RS Aggarwal Goyal Brothers ICSE Maths Solutions Ch-15)
Que-1: Define statistics as a subject.
Sol: It is a science which dals with the collection, presentations, analysis and interpretation of numerical data.
Que-2: What are the primary data and secondary data? Which of the two are more reliable and why?
Sol: (i) Primary data : The data collected by the investigator himself with a definite plan in mind are known as primary data.
(ii) Secondary data : The data collected by someone, other than the investigator are known as secondary data.
Que-3: Fill in the banks :
(i) The difference between the maximum and minimum observations in a data is called the …………. of the data.
(ii) The number of observations in a class-interval is called the …………… of the interval.
(iii) The mid-point of a class-interval is called the ……………… of the interval.
(iv) Lower-limit of the class-interval 24-30 is ………………. .
(v) Upper limit of the class-interval 16-20 is …………….. .
(vi) The class-mark of the class-interval 20-30 is …………… .
(vii) The class mark of the class-interval 9.5-19.5 is …………. .
Sol: (i) range
(ii) frequency
(iii) class-mark
(iv) 24
(v) 20
(vi) 25
(vii) 14.5
Que-4: Find the range of the data :
(a) 5,7,16,21,8,10 (b) 11,13,17,14,19,14,15,18
Sol: (i) Highest value = 21
minimum value = 11
so range is 21 – 5 = 16
(ii) Highest value = 19
minimum value = 11
so range is 19 – 11 = 8
Que-5: The class marks of a frequency distribution are 28,34,40,46,52. Find the class-size and all the class-intervals.
Sol: Class – size = 34 – 28 = 6
first class interval will be 25 – 31
similar other class interval will be
31 – 37, 37 – 43, 43 – 49, and 49 – 55 .
Que-6: State which of the following variables are continuous and which are discrete :
(i) Marks obtained by the students of a class in a test.
(ii) Daily maximum temperature of a city.
(iii) I.Q. of students of a class.
(iv) Weights of players of a Volley-ball team.
(v) Number of car-accidents in a city.
(vi) Distance travelled by a train.
(vii) Time taken by runners in a race
(viii) Sizes of shoes sold in a shoe-store.
(ix) Number of patients in a hospital per day.
Sol: (i) Discrete
(ii) Continuous
(iii) Continuous
(iv) Continuous
(v) Discrete
(vi) Continuous
(vii) Continuous
(viii) Discrete
(ix) Discrete
Que-7: Define the following terms :
(i) Variable (ii) Class-interval (iii) Class-size (iv) Class-mark (v) Class-limits (vi) True class-limits (vii) Frequency of a class (viii) Cumulative frequency of a class
Sol: (i) Variable : A quantity which can take different value is called a variable.=
(ii) Class Interval : Data can be grouped into class intervals such that all observations in that range belong to that class.
Class width = upper class limit – lower class limit
(iii) Class- size : The difference of true upper limits and true lover limit is called class size
(iv) Class-mark : 1/2 (lower + upper limit ) is called class marks.
(v) Class-limits : Each class interval is bounded by two figure, called limits.
(vi) True class-limits : Is continuous interval, the limits of the class is called true class limits.
(vii) Frequency of a class : The number of times an observation in a class, occurs is called its frequency.,
(viii) Cumulative frequency of class : The sum of the frequency of all the previous classes and that particular class, is called cumulative frequency of the class.
Que-8: Following data gives the number of children in 40 families :
,2,6,5,1,3,2,6,2,3,4,20,4,4,3,2,2,0,0,1,2,2,4,4,3,2,1,0,5,1,2,4,3,4,1,1,6,2,2
Represent it in the form of a frequency distribution.
Sol: Frequency Distribution of the given data :
Que-9: The marks obtained by 40 students of a class in an examination are given below. Present the data in the form of a frequency distribution using equal class-size, one such class being 10-15 (15 not included).
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, 10,16,8,16,17,8,23,21,6,23,15
Sol: Frequency Distribution of the given data :
Que-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
Sol: Frequency Distribution of the given data :
Que-11: The weekly wages (in rupees) of 30 workers in a factory are given below :
630,635,690,610,635,636,639,645,698,690,620,660,632,633,655,645,604, 608, 612, 640, 685, 635, 636,678, 640,668, 690,606,640, 690
Represent the data in the form of a frequency distribution with class size 10.
Sol: From the given data :
Lowest data = 604
Largest data = 698.
Range = 698-604 = 94.
Que-12: The weights in grams of 50 apples picked at random from a consignment are as follows :
131,113,82,75,204,81,84,118,104,110,80,107,111,141,136,123,90,78,90, 115, 110, 98, 106, 99, 107,84,76,186,82,100,109,128,115,107,115,119,93,187,139,129,130,68,195,123,125,111,92,86,70,126
From the grouped frequency table by dividing the variable range into intervals of equal width of 20g.
Sol: Smallest weight = 68 gm
Largest weight = 204 gm
range = 204-68 = 136
Width of each class interval is 20 gm
Frequency table are given below :
Que-13: The marks obtained by 35 students in an examination are given below:
370, 290, 318, 175, 170, 410, 378, 405, 380, 375, 315, 305, 325, 275, 241, 288, 261, 355, 402, 380, 178, 253, 428, 240, 210, 175, 154, 405, 380, 370,306,460, 328,440, 425
From a cumulative frequency table with class intervals of length 50.
Sol: Smallest marks = 154
Largest marks = 460
Range = 460-154 = 306
Cumulative frequency table is given below :
Que-14: Construct the cumulative frequency table from the frequency table given below :
Sol: Cumulative frequency table from the given frequency table :
Que-15: Construct a frequency distribution table from the following cumulative frequency distribution :
Sol: Cumulative frequency table from the given frequency distribution table :
Que-16: Construct a frequency table from the following data :
Sol: Frequency table of the given data :
Que-17: Convert the following frequency distribution to exclusive form :
Use this table to find:
(i) The true class-limits of the fourth class-interval.
(ii) The class-boundaries of the fifth class-interval
(iii) The class-mark of the third class-interval
(iv) The class-size of the sixth class-interval.
Sol: Frequency distribution to inclusive form of the given frequency distribution :
(i) The true class limits of the fourth class interval
is 44.5-49.5
(ii) The class-boundaries of the fifth class-interval
is 49.5-54.5
(iii) The class-mark of the third class-interval
= (39.5+44.5)/2 = 84/2 = 42.
(iv) The class-size of the sixth class-interval.
= 59.5 – 54.5 = 5.
–: End of Frequency Distribution Class 9 RS Aggarwal Exe-15 Goyal Brothers ICSE Maths Ch-15 :–
Return to : – RS Aggarwal Solutions for ICSE Class-9 Mathematics
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