**Exercise 22.1**

* **Q1) Define the following terms: *

*(i) Observations (ii) data *

*(iii) Frequency of an observation (iv) Frequency distribution *

**Solution:**

**(i) Observation** is the activity of paying close attention to someone or something in order to get information in numerical form.

**(ii) Data: **

The collection of observations is known as data.

**(iii) Frequency of an observation: **

The number of times an observation occurs in a given data is called the frequency of an observation.

**(iv) Frequency Distribution: **

It is a method of presenting raw data in a form that can be easily understood.

*Q2) 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 appealed? *

*(viii) How many have scored less than 50?*

**Solution:**

(i) Ascending order of the numbers in groups:

(30-39): 37, 39

(40 – 49): 44, 48, 48

(50 – 59): 50, 52, 53, 55, 56, 58, 58, 59

(60 – 69): 60, 60, 60, 61, 62, 64, 67, 68

(70 – 79): 70, 75, 77, 78

(80 – 89): 84, 88

(90 – 99): 90, 98

(100-109): 100

(ii) The highest score is 100.

(iii) The lowest score is 37.

(iv) Range is = Maximum observation – Minimum observation.

= 100 – 37 = 63.

(v) If 40 is the pass mark, then only 2 students have failed.

(vi) 8 students have scored 75 or more.

(vii) 51, 54 and 57 are not there between 50 and 60.

(viii) 5 students scored less than 50.

*Q3) 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 weigh more than 2.8? *

*(viii) How many babies weigh 2.8 kg? *

**Solution: **

(i) Weights in descending order:

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

(ii) Highest weight: 3.1 Kg.

(iii) Lowest weight: 2.1 Kg.

(iv) Range = Maximum observation – Minimum observation

= (3.1-2.1) kg = 1.0 Kg.

(v) A total of 15 babies were born on that day.

(vi) 4 babies weigh below 2.5 kg.

(vii) 4 babies weigh more than 2.8 kg.

(viii) 2 babies weigh 2.8 kg.

*Q4) 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:**

Required frequency-distribution table:

Number of children | Frequency |

0 | 5 |

1 | 7 |

2 | 11 |

3 | 5 |

4 | 6 |

5 | 3 |

6 | 3 |

* **Q5) 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:**

<

Marks | No. of Students |

7 | 2 |

14 | 1 |

16 | 1 |

17 | 1 |

19 | 1 |

21 | 1 |

22 | 1 |

27 | 2 |

29 | 1 |

31 | 1 |

33 | 2 |

34 | 1 |

37 | 4 |

38 | 2 |

39 | 4 |

41 | 1 |

42 | 6 |

43 | 1 |

44 | 1 |

47 | 1 |

49 | 1 |

51 | 3 |

52 | 1 |

53 | 3 |

54 | 1 |

57 | 1 |

59 | 2 |

61 | 1 |

62 | 1 |

67 | 1 |

*Q6) 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:**

Score | Number of Times |

1 | 5 |

2 | 5 |

3 | 4 |

4 | 3 |

5 | 4 |

6 | 4 |

*Q7) 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:**

Required frequency-distribution table:

Number of Accidents | Number of Days |

0 | 2 |

1 | 3 |

2 | 6 |

3 | 3 |

4 | 4 |

5 | 6 |

6 | 6 |

*Q8) 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:**

Frequency Distribution Table is:

Ages (in years) | Number of Students |

12 | 4 |

13 | 12 |

14 | 9 |

15 | 2 |

16 | 2 |

17 | 1 |

*Q9) 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:**

Frequency Distribution Table is

Wages (in Rs.) | Number of Workers |

150 | 3 |

200 | 5 |

250 | 4 |

300 | 2 |

350 | 1 |

(i) The range in wages (in Rs.) = 350 – 150 = 200.

(ii) Only 1 worker is getting Rs. 350.

(iii) 3 workers are getting the minimum wages, i.e., Rs. 150.

*Q10) 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:**

Required frequency-distribution table:** **

Marks | Frequency |

9 | 6 |

12 | 4 |

17 | 4 |

18 | 2 |

19 | 4 |

20 | 3 |

25 | 2 |

(i) Range of marks: 25 – 9 = 16.

(ii) The highest mark is 25.

(iii) 9 is occurring most frequently.

*Q11) 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 6 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:**

The Frequency Distribution Table is:

Marks | Tally Marks | Frequency |

1 | ll | |

2 | lll | |

3 | lll | |

4 | ||

5 | ||

6 | ||

7 | 5 | |

8 | llll | 4 |

9 | lll | 3 |

(i) 12 students obtained marks equal to or more than 7.

(ii) Only 8 students obtained marks below 4.

*Q12) 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:**

Sweet | Tally Marks | Frequency |

Ladoo | 12 | |

Barfi | lll | 3 |

Jalebi | 6 | |

Rasgulla | 9 |

(ii) Ladoo is preferred by most of the students, 12 students.