SELINA Solutions for Class 9 Maths Chapter 18  Statistics
Chapter 18  Statistics Exercise Ex. 18(A)
(a)Discrete variable.
(b)Continuous variable.
(c)Discrete variable.
(d)Continuous variable.
(e)Discrete variable.
The frequency table for the given distribution is
Marks 
Tally Marks 
Frequency 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
The frequency table for the given distribution is
Marks 
Tally Marks 
Frequency 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
_{} 
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.
(a)Variable.
(b)Discrete variables.
(c)Continuous variable.
(d)The range is _{}
(e)Lower limit is _{} and upper limit is _{}
(f)The class mark is _{}
_{}
In case of frequency 10  19 the lower class limit is 10, upper class limit is 19 and midvalue is
In case of frequency 20  29 the lower class limit is 20, upper class limit is 29 and midvalue is
In case of frequency 30  39 the lower class limit is 30, upper class limit is 39 and midvalue is
In case of frequency 40  49 the lower class limit is 40, upper class limit is 49 and midvalue is
In case of frequency 1.1  2.0 the lower class limit is 1.1, upper class limit is 2.0 and class mark
is
In case of frequency 2.1  3.0 the lower class limit is 2.1, upper class limit is 3.0 and class mark
is
In case of frequency 3.1  4.0 the lower class limit is 3.1, upper class limit is 4.0 and class mark
is
(a)
The actual class limit of the fourth class will be:
44.549.5.
(b)
The class boundaries of the sixth class will be:
54.559.5
(c)
The class mark of the third class will be the average of the lower bound and the upper bound of the interval. Therefore class mark will be:
(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.
(i)The cumulative frequency distribution table is
C.I 
c.f 
_{} _{} _{} _{} _{} 
_{} _{} _{} _{} _{} 
(ii)The cumulative frequency distribution table is
C.I 
c.f 
_{} _{} _{} _{} _{} 
_{} _{} _{} _{} _{} 
(i)The frequency distribution table is
C.I 
c.f 
_{} _{} _{} _{} 
_{} _{} _{} _{} 
(ii)The frequency distribution table is
C.I 
c.f 
_{} _{} _{} _{} _{} 
_{} _{} _{} _{} _{} 
The frequency table is
C.I 
c.f 
_{} _{} _{} _{} _{} _{} 
_{} _{} _{} _{} _{} _{} 
The frequency distribution table is
C.I 
c.f 
_{} _{} _{} _{} 
_{} _{} _{} _{} 
(i)The number of students in the age group _{} is _{}
(ii)The age group which has the least number of students is _{}
Class Interval 
Frequency 
Cumulative Frequency 
_{} _{} _{} _{} 6574 _{} 
_{} _{} _{} _{} _{} _{} 
_{} _{} _{} _{} _{} _{} 
X 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
F 
2 
5 
5 
8 
4 
5 
4 
4 
5 
8 
Most occurring digits are 3 and 9. Least occurring digits are 0.
Chapter 18  Statistics Exercise Ex. 18(B)
The frequency polygon is shown in the following figure
Steps:
(i)Drawing a histogram for the given data.
(ii)Marking the midpoint at the top of each rectangle of the histogram drawn.
(iii)Also, marking midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
(iv)Joining the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
Steps:
 Draw a histogram for the given data.
 Mark the midpoint at the top of each rectangle of the histogram drawn.
 Also, mark the midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
 Join the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
The required combined histogram and frequency polygon is shown in the following figure:
The class intervals are inclusive. We will first convert them into the exclusive form.
ClassInterval 
Frequency 
9.5  14.5 
5 
14.5  19.5 
8 
19.5  24.5 
12 
24.5  29.5 
9 
29.5  34.5 
4 
Steps:
 Draw a histogram for the given data.
 Mark the midpoint at the top of each rectangle of the histogram drawn.
 Also, mark the midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
 Join the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
The required frequency polygon is as follows:
Steps:
 Draw a histogram for the given data.
 Mark the midpoint at the top of each rectangle of the histogram drawn.
 Also, mark the midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
 Join the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
The required frequency polygon is as follows:
(a) Using Histogram:
C.I. 
f 
10  30 
4 
30  50 
7 
50  70 
5 
70  90 
9 
90  110 
5 
110  130 
6 
130  150 
4 
Steps:
 Draw a histogram for the given data.
 Mark the midpoint at the top of each rectangle of the histogram drawn.
 Also, mark the midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
 Join the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
(b) Without using Histogram:
Steps:

Find the classmark (midvalue) of each given classinterval.
 On a graph paper, mark classmarks along Xaxis and frequencies along Yaxis.

On this graph paper, mark points taking values of classmarks along Xaxis and the values of their corresponding frequencies along Yaxis.
 Draw line segments joining the consecutive points marked in step (3) above.
C.I. 
Classmark 
f 
10  10 
0 
0 
10  30 
20 
4 
30  50 
40 
7 
50  70 
60 
5 
70  90 
80 
9 
90  110 
100 
5 
110  130 
120 
6 
130  150 
140 
4 
150  170 
160 
0 
Using Histogram:
C.I. 
f 
5  15 
8 
15  25 
16 
25  35 
18 
35  45 
14 
45  55 
8 
55  65 
2 
Steps:
 Draw a histogram for the given data.
 Mark the midpoint at the top of each rectangle of the histogram drawn.
 Also, mark the midpoint of the immediately lower classinterval and midpoint of the immediately higher classinterval.
 Join the consecutive midpoints marked by straight lines to obtain the required frequency polygon.
Without using Histogram:
Steps:

Find the classmark (midvalue) of each given classinterval.
 On a graph paper, mark classmarks along Xaxis and frequencies along Yaxis.
 On this graph paper, mark points taking values of classmarks along Xaxis and the values of their corresponding frequencies along Yaxis.
 Draw line segments joining the consecutive points marked in step (3) above.
C.I. 
Classmark 
f 
5  5 
0 
0 
5  15 
10 
8 
15  25 
20 
16 
25  35 
30 
18 
35  45 
40 
14 
45  55 
50 
8 
55  65 
60 
2 
65  75 
70 
0 
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