Ex-21.1, Data Handling Presentation Of Data, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

Clear all your Class 6 doubts with EduRev Join for Free

Join for Free

Q. 1. Define the following terms:

(i) Observation

(ii) data

(iii) Frequency of an observation

(iv) Frequency distribution

Sol: (i) Observation is the active acquisition of information from a primary source.

(ii) A collection of facts such as values measurements are called data.

(iii) Number of times an observation has occurred in a given data.

(iv) A frequency distribution is an arrangement of instances in which a variable takes each of its possible values. A frequency distribution depicts a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in those classes.

Q. 2. The final marks in mathematics of 30 students are as follows:

53, 61, 48, 60, 78, 68, 55, 100, 67, 95

75, 88, 77, 37, 84, 58, 60, 48, 62, 56

44, 58, 52, 64, 98, 59, 70, 39, 50, 60

(i) Arrange these marks in ascending order. 30 to 39 one group, 40 to 49 second group, etc

(ii) What is the highest score?

(iii) What is the lowest score?

(iv) What is the range?

(v) If 40 is the pass mark, how many have failed?

(vi) How many have scored 75 or more?

(vii) Which observations between 50 and 60 have not appeared?

(viii) How many have scored less than 50?

Sol: (i) Frequency distribution of the given marks in mathematics of 30 students

(ii) From the given data, we can see that the highest score is 100.

(iii) The above data shows 37 as the lowest score.

(iv) Range = highest score – lowest score = 100 – 37 = 63

(v) If 40 is the pass mark, students who have scored less than 40 have failed. So, the students who have scored 37 and 39 have failed.

Therefore, the number of students that have failed in the exam = 2

(vi) Students who have scored 75, 77, 78, 84, 88, 90, 98, and 100 are the ones to score more than 75

Therefore, the number of students who scored 75 or more = 8

(vii) The observations 51, 5,4 and 57 have not appeared in the data range of 50 – 60.

(viii) Students who have scored 37, 39, 44, 4,8 and 48 are the ones to score less than 50

Therefore, the number of students who got less than 50 = 5

Q. 3. The weights of newborn babies (in kg) in a hospital on a particular day are as follows:

2.3, 2.2, 2.1, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4

(i) Rearrange the weights in descending order.

(Ii) Determine the highest weight.

(iii) Determine the lowest weight.

(iv) Determine the range.

(v) How many babies were born on that day?

(vi) How many babies weigh below 2.5 kg?

(vii) How many babies weigh more than 2.8 kg?

(viii) How many babies weigh 2.8 kg?

Sol: (i) Arranging the weights of the newborn babies in descending order, we get 3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1,

(ii) In a descending order, the first number is always the highest.

Therefore, the highest weight = 3.1 kg.

(iii) In a descending order, the last number is always the lowest

Therefore, lowest weight = 2.1 kg

(iv) Range = Highest weight – lowest weight

= 3.1 kg – 2.1 kg = 1.0 kg

(v) We can count the number of babies born on that particular day by counting the number of observations.

Therefore, the number of babies born on that day = 15.

(vi) Babies who weigh 2.1, 2.2, 2.3, and 2.4 kg are the ones to weigh less than 2.5 kg.

(vii) Babies which weigh 2.9, 2.9, 3.,0 and 3.1 kg are the ones to weigh more than 2.8 kg.

(viii) Number of babies weighing 2.8 kg = 2

Q. 4. The 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, 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

Represent it in the form of a frequency distribution.

Sol:  The Frequency distribution of the given data:

Q. 5. Prepare a frequency table of the following scores obtained by 50 students in a test

42 51 21 42 37 37 42 49 38 52

7 33 17 44 39 7 14 27 39 42

42 62 37 39 67 51 53 53 59 41

29 38 27 31 54 19 53 51 22 61

42 39 59 47 33 34 16 37 57 43

Sol: Frequency distribution table of the given scores:

Q. 6. A die was thrown 25 times, and the following scores were obtained

1 5 2 4 3

6 1 4 2 5

1 6 2 6 3

5 4 1 3 2

3 6 1 5 2

Sol: The Frequency distribution table of the given data:

Q. 7. In a study of several accidents per day, the observations for 30 days were obtained as follows :

6 3 5 6 4 3 2 5 4 2

4 2 1 2 2 0 5 4 6 1

6 0 5 3 6 1 5 5 2 6

Prepare a frequency distribution table

Sol: The Frequency distribution table of the given number of accidents per day is given below:

Q. 8. Prepare a frequency table of the following ages (in years) of 30 students of class VIII in your school:

13, 14, 13, 12, 14, 13, 14, 15, 13, 14, 13, 14, 16, 12, 14

13, 14, 15, 16, 13, 14, 13, 12, 17, 13, 12, 13, 13, 13, 14

Sol: Frequency distribution table of the given ages (in years) of 30 students:

Q. 9. Following figures relate the weekly wages (in Rs) of 15 workers in a factory:

300, 250, 200, 250, 200, 150, 350, 200, 250, 200, 150, 300, 150, 200, 250

Prepare a frequency table

(i) What is the range in wages (in Rs)?

(ii) How many Workers are getting RS 350?

(iii) How many workers are getting the minimum wage?

Sol: Frequency distribution of the given weekly wages of 15 workers:

(i) Minimum wages = Rs. 150

Maximum wage = Rs. 350

Therefore, Range = Maximum wage – Minimum wage

= Rs. 350 – Rs. 150

= Rs. 200

(ii) Number of workers getting Rs. 350 = 1 worker

(iii) Here, the Minimum wage is Rs. 150

Number of workers getting Rs. 150 = 3 workers

Therefore, the number of workers getting minimum wages = 3 workers.

Q. 10. Construct a frequency distribution table for the following marks obtained by 25 students in a history test in class VI of a school:

9, 17, 12, 20, 9, 18, 25, 17, 19, 9, 12, 9, 18, 17, 19, 20, 25, 9, 12, 17, 19, 19, 20, 9

(i) What is the range of marks?

(ii) What is the highest mark?

(iii) Which mark is occurring more frequently?

Sol: Now, we arrange these marks in ascending order: 9, 9, 9, 9, 12, 12, 12, 17, 17, 17, 17, 18, 18, 19, 19, 19, 19, 20, 20, 20, 25, 25

(i)The range of a data set is the difference between the highest and lowest values.

• Lowest mark = 9
• Highest mark = 25
• Range=Highest value−Lowest value
• $25-9=16$

(ii) From our arranged data, the highest mark is 25.

(iii) The frequency distribution table shows that 9 appears 6 times, which is the highest frequency.

So, the most frequently occurring mark is 9.

Q. 12. Following is the choice of sweets of 30 students of class VI: Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo, Barfi, Rasgulla, Rasgulla, Ladoo.

(i) Arrange the names of sweets in a table using tally marks

(ii) Which sweet is preferred by most of the students?

Sol: (i) Frequency distribution of the given sweets:

(ii) The frequency of Ladoo is 12, i.e., maximum

Therefore, Ladoo is the sweet that is preferred by most of the students.