SELINA Solution Class 9 Chapter 18 Statistics Exercise 18A

Question 1

State, the following variable is continuous or discrete:
number of children in your class.

Ans:Discrete Variable Question 1.2

State, the following variable is continuous or discrete:
Distance travelled by car.

Ans:Continous Variable Question 1.3

State, the following variable is continuous or discrete:
Sizes of shoes.

Ans:Discrete Variable Question 1.4

State, the following variable is continuous or discrete: Time.

Ans:Continous Variable Question 1.5

State, the following variable is continuous or discrete: Number of patients in a hospital.

Ans:Discrete Variable Question 2

Given below are the marks obtained by 30 students in an examination:

08	17	33	41	47	23	20	34
09	18	42	14	30	19	29	11
36	48	40	24	22	02	16	21
15	32	47	44	33	01

Taking class intervals 1 - 10, 11 - 20, ....., 41 - 50;
make a frequency table for the above distribution.

Sol:

The frequency table for the given distribution is

Marks	Tally Marks	Frequency
1 - 10		4
11 - 20		8
21 - 30		6
31 - 40		6
41 - 50		6

Question 3

The marks of 24 candidates in the subject mathematics are given below:

45	48	15	23	30	35	40	11
29	0	3	12	48	50	18	30
15	30	11	42	23	2	3	44

The maximum marks are 50. Make a frequency distribution taking class intervals 0 - 10, 10-20, .......

Sol:

The frequency table for the given distribution is

Marks	Tally Marks	Frequency
0 - 10	||||	4
10 - 20		6
20 - 30	|||	3
30 - 40	||||	4
40 - 50		7

In this frequency distribution, the marks 30 are in the class of interval 30 - 40 and not in 20 - 30. Similarly, marks 40 are in the class of interval 40 - 50 and not in 30 - 40.

Question 4.1

Fill in the blank :
 A quantity which can very from one individual to another is called a ............. 

Sol:

A quantity which can very from one individual to another is called a Variable.

Question 4.2

Fill in the blank :
Sizes of shoes are ........... variables.

Sol:

Sizes of shoes are Discrete variables.

Question 4.3

Fill in the blank :
Daily temperatures is ........... variable.

Daily temperatures is Continuous  variable.

Sol:

Daily temperatures is Continuous  variable.

Question 4.4

Fill in the blank :
The range of data 7, 13, 6, 25, 18, 20, 16 is ............

Sol:

The range of the data 7, 13, 6, 25, 18, 20, 16 is The range is 25 - 6 = 19.

Question 4.5

Fill in the blank : 
In the class interval 35 - 46; the lower limit is .......... and the upper limit is .........

Sol:

In the class interval 35 - 46; the lower limit is 35 and the upper limit is 46.

Question 4.6

Fill in the blank :
The class mark of class interval 22 - 29 is ...........

Sol:

The class mark of class interval 22 - 29 is
The classmark is  22 - 29 = ${\displaystyle \frac{22+29}{2}=\frac{51}{2}}$ = 25.5.

Question 5

Find the actual lower class limits, upper-class limits and the mid-values of the classes:
10 - 19, 20 - 29, 30 - 39 and 40 - 49.

Sol:

In case of frequency 10 - 19 the lower class limit is 10, the upper class limit is 19 and mid-value is
${\displaystyle \frac{10+19}{2}}$ = 14.5

In case of frequency 20 - 29 the lower class limit is 20, the upper class limit is 29 and mid-value is
${\displaystyle \frac{20+29}{2}}$ = 24.5

In case of frequency 30 - 39 the lower class limit is 30, the upper class limit is 39 and mid-value is
${\displaystyle \frac{30+29}{2}}$ = 34.5

In case of frequency 40 - 49 the lower class limit is 40, the upper class limit is 49 and mid-value is
${\displaystyle \frac{40+49}{2}}$ = 44.5

Question 6

Find the actual lower and upper-class limits and also the class marks of the classes:
1.1 - 2.0, 2.1 -3.0 and 3.1 - 4.0.

Sol:

In the case of frequency 1.1 - 2.0 the lower class limit is 1.1, upper-class limit is 2.0 and classmark

is  ${\displaystyle \frac{1.1+2.0}{2}}$ = 1.55

In the case of frequency 2.1 - 3.0 the lower class limit is 2.1, upper-class limit is 3.0 and classmark

is  ${\displaystyle \frac{2.1+3.0}{2}}$ = 2.55

In the case of frequency 3.1 - 4.0 the lower class limit is 3.1, the upper class limit is 4.0 and classmark

is  ${\displaystyle \frac{3.1+4.0}{2}}$ = 3.55

Question 7

Use the table given below to find:
(a) The actual class limits of the fourth class.
(b) The class boundaries of the sixth class.
(c) The class mark of the third class.
(d) The upper and lower limits of the fifth class.
(e) The size of the third class.

Class Interval	Frequency
30 - 34	7
35 - 39	10
40 - 44	12
45 - 49	13
50 - 54	8
55 - 59	4

SOl:

(a) The actual class limit of the fourth class will be  44.5 - 49.5.

(b) The class boundaries of the sixth class will be 54.5 - 59.5

(c) The class mark of the third class will be the average of the lower bound and the upper bound of the interval. Therefore the class mark will be: ${\displaystyle \frac{40+44}{2}}$ = 42

(d) The upper and lower limit of the fifth class is 54 and 50 respectively.

(e) The size of the third class will be 44 - 40 + 1 = 5.

Question 8.1

Construct a cumulative frequency distribution table from the frequency table given below:

Class Interval	Frequency
0 -8	9
8 - 16	13
16 - 24	12
24 - 32	7
32 - 40	15

sOL:

 The cumulative frequency distribution table is

C.I	c.f
0 -8	9
8 - 16	22
16 - 24	34
24 - 32	41
32 - 40	56

Question 8.2

Construct a cumulative frequency distribution table from the frequency table given below:

Class Interval	Frequency
1 - 10	12
11 - 20	18
21 - 30	23
31 - 40	15
41 - 50	10

SOl:

The cumulative frequency distribution table is

C.I	c.f
1 - 10	12
11 - 20	30
21 - 30	53
31 - 40	68
41 - 50	78

Querstion 9.1

Construct a frequency distribution table from the following cumulative frequency distribution:

Class Interval	Cumulative Frequency
10 - 19	8
20 - 29	19
30- 39	23
40- 49	30

Sol:

The frequency distribution table is

C. I	c.f
10 - 19	8
20 - 29	11
30 - 39	4
40 - 49	7

Question 9.2

Construct a frequency distribution table from the following cumulative frequency distribution:

C.I	C.F
5 - 10	18
10 - 15	30
15 - 20	46
20 - 25	73
25 - 30	90

Sol:

The frequency distribution table is

C .I	c.f
5 -  10	18
10 - 15	12
15 - 20	16
20  - 25	27
25 - 30	17

Question 10

Construct a frequency table from the following data:

Marks	No. of students
less than 10	6
less than 20	15
less than 30	30
less than 40	39
less than 50	53
less than 60	70

SOl:

The frequency table is

C. I	c.f
0 - 10	6
10 - 20	9
20 - 30	15
30 - 40	9
40 - 50	14
50 - 60	17

Question 11

Construct the frequency distribution table from the following cumulative frequency table:

Ages	No. of students
Below 4	0
Below 7	85
Below 10	140
Below 13	243
Below 16	300

(i) State the number of students in the age group 10 - 13.
(ii) State the age-group which has the least number of students.

Sol:

The frequency distribution table is

C. I	c.f
4 -  7	85
7 - 10	55
10 -  13	103
13 - 16	57

(i)The number of students in the age group  is 10 -13 is 103

(ii)The age group which has the least number of students is  7 - 10

Question 12

Fill in the blank in the following table:

Class interval	Frequency	Cumulative Frequency
25 - 34	......	15
35 - 44	......	28
45 - 54	21	......
55 - 64	16	......
65 - 74	......	73
75 - 84	12	......

Sol: (To be added) Question 13

Fill in the blank in the following table:

Class interval	Frequency	Cumulative Frequency
25 - 34	......	15
35 - 44	......	28
45 - 54	21	......
55 - 64	16	......
65 - 74	......	73
75 - 84	12	......

Sol:

Fill in the blank in the following table:

Class interval	Frequency	Cumulative Frequency
25 - 34	......	15
35 - 44	......	28
45 - 54	21	......
55 - 64	16	......
65 - 74	......	73
75 - 84	12	......