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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