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:

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 order
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) 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 number 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 children	Tally 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 –

Marks	Tally marks	Number of Students (frequency)	Marks	Tally 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 –

Die	Tally 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 accidents	Tall 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-

Marks	Tally 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.