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

**(i) Observations**

**Solution:**

Observation is the value of a particular variable at a particular period.

OR

Each entry in the given data is called an observation.

**(ii) Raw data**

**Solution:**

Raw data is the data collected in its original form.

OR

Raw data is a collection of observations by an observer.

**(iii) Frequency of an observation**

**Solution:**

Frequency of an observation is the number of times a certain value or a class of values occurs in the given data.

**(iv) Frequency distribution**

**Solution:**

Frequency distribution is the organization of raw data in table form with classes and frequencies.

**(v) Discrete frequency distribution**

**Solution:**

Discrete frequency distribution is a frequency distribution where sufficiently great numbers are grouped into one class.

**(vi) Grouped frequency distribution**

**Solution:**

Grouped frequency distribution is a frequency distribution where several numbers are grouped into one class.

**(vii) Class-interval**

**Solution:**

Class interval is a group under which large number of data is grouped to analyze its Range and Distribution.

**(viii) Class-size**

**Solution:**

The difference between the upper and lower values of a class is called class-size.

**(ix) Class limits**

**Solution:**

Class limits are the smallest and the largest observations in a class. Every class has two limits – upper limit and lower limit.

**(x) True class limits**

**Solution:**

True class limits are the actual class limits of a class.

**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.**

**Now answer the following:**

**(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:**

(i)The given marks can be arranged in the ascending order as –

Groups

(class-interval)Marks arranged in ascending order30 – 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)The range is 100 – 37 = 63.(v)If 40 is the pass marks then the number of failed candidates = 2 (37, 39).(vi)The number of students who scored 75 or more = 8 (75, 77, 78, 84, 88, 90, 98, 100).(vii)The marks 51, 54 and 57 do not actually appear between 50 and 60.(viii)The umber of students who scored less than 50 = 5 (37, 39, 44, 48, 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 weigh more than 2.8 kg?**

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

**Solution:**

(i)The weights of the newly born babies in descending order are as follows –

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)The highest weight is 3.1 kg.(iii)The lowest weight is 2.1 kg.(iv)The range is 3.1-2.1 = 1 kg(v)The number of babies born on that day is 15.(vi)The number of babies who weighs below 2.5 kg is 4 (2.4, 2.3, 2.2, 2.1)(vii)The number of babies who weighs more than 2.8 kg is 4 (3.1, 3.0, 2.9, 2.9)(viii)The number of babies whose weight is 2.8 kg is 2.

**Question 4: Following data gives the number of children in 41 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, 2.**

**Represent it in the form of a frequency distribution.**

**Solution:**

The data can be represented in the form of frequency distribution in following way –

Number of childrenTally marks

Number of families

(frequency)0 ~~||||~~5 1 ~~||||~~||7 2 ~~||||~~~~||||~~||12 3 ~~||||~~5 4 ~~||||~~|6 5 ||| 3 6 ||| 3

**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:**

The frequency table of scores obtained by 50 students in a test can be shown as –

MarksTally marks

Number of Students

(frequency)MarksTally marks

Number of Students

(frequency)7 || 2 41 | 1 14 | 1 42 ~~||||~~|6 16 | 1 43 | 1 17 | 1 44 | 1 19 | 1 47 | 1 21 | 1 49 | 1 22 | 1 51 ||| 3 27 || 2 52 | 1 29 | 1 53 ||| 3 31 | 1 54 | 1 33 || 2 57 | 1 34 | 1 59 || 2 37 |||| 4 61 | 1 38 || 2 62 | 1 39 |||| 4 67 | 1

**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:**

The frequency table of the scores obtained when a die is thrown can be shown as –

DieTally marks

Scores

(frequency)1 ~~||||~~5 2 ~~||||~~5 3 |||| 4 4 ||| 3 5 |||| 4 6 |||| 4

**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:**

The frequency distribution table of the number of accidents per day for a period of 30 days can be shown as –

Number of accidentsTall marks

Number of days

(frequency)0 || 2 1 ||| 3 2 ~~||||~~|6 3 ||| 3 4 |||| 4 5 ~~||||~~|6 6 ~~||||~~|6

**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:**

The frequency table of the ages of 30 students of class VIII in the school can be shown as –

Age (In Years)Tally marks

Number of students

(frequency)12 |||| 4 13 ~~||||~~~~||||~~||12 14 ~~||||~~||||9 15 || 2 16 || 2 17 | 1

**Question 9: Following figures relate to 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:**

The frequency table of the weekly wages of 15 workers in a factory can be shown as –

Wages (In Rs.)Tally marks

Number of workers

(frequency)150 ||| 3 200 ~~||||~~5 250 |||| 4 300 || 2 350 | 1

(i)The range of wages (in Rs.) is 350-150 = 200.(ii)The number of workers getting Rs. 350 is 1(iii)Here, The minimum wage is 150. So, the number of workers earning minimum wages is 3.

**Question 10: Construct a frequency distribution table for the following marks obtained by 25 students in a history test in class VIII 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:**

The frequency distribution table of the marks obtained by 25 students in a history test in class VIII of a school can be shown as-

MarksTally marks

Number of students

(frequency)9 ~~||||~~|6 12 |||| 4 17 |||| 4 18 || 2 19 |||| 4 20 ||| 3 25 || 2

(i)The range of marks is 25-9 = 16.(ii)The highest mark is 25.(iii)The mark that occurs most frequently is 9. It occurs 6 times.

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