Question 1: Define the following terms:
(i) Observations
(ii) Data
(iii) Frequency of an observation
(iv) Frequency distribution
Solution 1:
(i) Observation:- The addition of information from obtained from primary sources.
(ii) Data:- Collection of facts and information as values measurements.
(iii) Frequency of an observation:- Repetition of an observation in the given data.
(iv) Frequency distribution:- Frequency distribution is a table of present raw details in column and Raw.
Question 2: The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90
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 the 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 actually appeared?
(viii) How many have scored less than 50?
Solution 2:
(i) Frequency distribution table of the marks obtained in Mathematics by students:
(ii) 100 is the highest score from the given data.
(iii) 37 is the lowest score from the above data.
(iv) Range = Highest Value – Lowest Value
Range = 100 – 37
Range = 63
(v) 40 is the passing marks, Students who scored 37 and 39 have failed.
Thus, Number of failed students have 2.
(vi) From the given data numbers of students have scored 75 or more are 8.
(vii) 51, 54 and 57 have not appeared in the range of 50 – 60.
(viii) From the above data we know that 5 students have scored less than 50 i.e. 37, 39, 44, 48 and 48.
Question 3: The weights of new born babies (in kg) in a hospital on a particular day are as follows:
2.3, 2.2, 2.1, 2.7, 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 weight more than 2.8 kg?
(viii) How many babies weight 2.8 kg?
Solution 3:
(i) 3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1
Above are the weights in descending order.
(ii) 3.1kg is the highest weight according to the given data.
(iii) 2.1kg is the lowest weight according to the given data.
(iv) Range = Highest weight – Lowest weight
Range = 3.1 – 2.1
Range = 1.0 kg
(v) 15 babies were born on that day.
(vi) Weight below 2.5 kg is 2.1, 2.2, 2.3 and 2.4 kg.
Thus, 4 babies weigh below 2.5 kg.
(vii) Weight more than 2.8 kg are 2.9, 2.9, 3.0 and 3.1 kg.
Thus, 4 babies weigh more than 2.8 kg.
(viii) 2 babies weight are 2.8 kg.
Question 4: 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.
Solution 4:
Question 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
Solution 5:
Question 6: A die was thrown 25 times and 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
Prepare a frequency table of the scores.
Solution 6:
Question 7: In a study of number of 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.
Solution 7:
Question 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.
Solution 8:
Question 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 wages?
Solution 9:
(i) Range = Maximum wage – Minimum wage
Range = 350 – 150
Range = Rs. 200
(ii) 1 worker is getting Rs. 350 as weekly wages.
(iii) Rs. 150 is the minimum weekly wages. Total 3 workers getting minimum wage.
Question 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, 12, 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?
Solution 10:
(i) Range = Highest marks – Lowest marks
Range = 25 – 9
Range = 16
(ii) 25 is the highest mark according to the frequency table.
(iii) 9 occur more frequently.
Question 11: In a mathematics test following marks were obtained by 40 students of class VI. Arrange these marks in a table using, tally marks.
8 1 3 7 6 5 5 4 4 2
4 9 5 3 7 1 6 5 2 7
7 3 8 4 2 8 9 5 8 6
7 4 5 6 9 6 4 4 6 6
(i) Find how many students obtained marks equal to or more than 7?
(ii) How many students obtained marks below 4?
Solution 11:
(i) From the frequency distribution table 3 students are equal to or more than 7.
Number of students = 5 + 4 + 3
Number of students = 12
(ii) From the frequency distribution table 4 students are obtained marks below 4:-
Number of students = 2 + 3 + 3
Number of students = 8
Question 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?
Solution 10:
(i) Frequency table of sweets given to 30 students is as follows:
(ii) Most preferred sweet for students in Ladoo.