**Exercise 22.1**

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**Question :1. Define the following terms:**

**(i) Observations**

**(ii) Data**

**(iii) Frequency of an observation**

**(iv) Frequency distribution**** **

**Solution 1:**

(i) **Observations:** The act of paying close attention to someone or something in order to obtain numerical data is known as observation.

(ii) **Data:** Data is a term that refers to a series of observations.

(iii) **Frequency of an observation:** The frequency of an observation is the number of times it occurs in a given set of data.

(iv) **Frequency distribution**: It's a way of viewing raw data in a way that's simple to comprehend.

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**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 appealed?**

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

**Solution 2:**

(i) Groups the number in ascending order:

(ii) 100 is the highest score.

(iii) 37 is the lowest score.

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

= 100 – 37

= 63.

(v) Just two students have failed if the pass mark is 40.

(vi) 8 students received a score of 75 or higher.

(vii) Between 50 and 60, there are no numbers 51, 54, or 57.

(viii) 5 students received a score of less than 50.

** **

**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 weigh more than 2.8?**

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

**Solution 3:**

(i) Descending order of weights:

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 is 3.1 Kg.

(iii) Lowest weight is 2.1 Kg.

(iv) Range = Maximum observation – Minimum observation

= (3.1-2.1) kg

= 1.0 Kg.

(v) On that particular day, 15 babies were born.

(vi) 4 of the babies are under 2.5 kg.

(vii) There are 4 babies weighing more than 2.8 kg.

(viii) There are 2 babies, each weighing 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:**

Required frequency table for given data is:

**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:**

Frequency table:

**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:**

Frequency table for given data:

**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:**

Frequency distribution table:

**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:**

Frequency distribution table is:

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

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

(iii) 3 employees are paid the minimum wage, which is Rs. 150.

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**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:**

Required frequency distribution table is:

(i) Range of marks: 25 – 9 = 16.

(ii) 25 is the highest mark.

(iii) 9 is occurring 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 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 11:**

(i) 10 students received a grade of 7 or higher.

(ii) Only 11 students received a grade of less than four.

**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 12:**

(ii) The majority of the 12 students prefer ladoo.