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CBSE 9th Standard Mathematics Statistics Model Questions Papers Study Material - QB365 Set A

Published on: 29/10/2025

Question Set A

CBSE 9th Standard Mathematics Statistics Model Questions Papers Study Material - QB365

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Std: 9th Standard CBSE - Mathematics

chapter: Statistics - Model Questions Papers

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Questions:

Generic 2

4 x 2 = 8

10 numbers 8,11,15,19,x+1,2x-13,28,31,40,41 are written in ascending order. If the median is 24, find x.

Find the median of the following data 15,28,72,56,44,32,31,43 and 51. If 32 is replaced by 23, find the new median.

The blood group of 30 students are recorded as follows:

A,	B,	O,	A,	AB,	O,
A	O,	B,	A,	O,	B,
A	AB,	B,	A,	AB,	B,
A,	A,	O,	A,	AB,	B,
A,	O,	B,	A,	B,	A

Prepare a freqeuncy distribution table for the data.

In a specific year, the distribution of the ages (in years) of primary teachers of a district is given:

Age (in years)	Number of teachers
15-20	10
20-25	30
25-30	50
30-35	50
35-40	30
40-45	6
45-50	4

(i) What is the lower limit of the first class interval?
(ii) What are the limits of the fourth class interval?
(iii) What is the class mark of the class 45-50?

Generic 3

5 x 3 = 15

Find the mode of 14,25,14,28,18,17,18,14,23,22,14,18

In a Mathematics test given to 15 students, the following marks (out of 100) are recorded:
41,39,48,52,46,62,54,40,96, 52,98,40,42,52,60
Find the mean, median and mode of this data.

The following table gives the distribution of students of two sections according to the marks obtained by them:

Section A Section B
Marks	Freqeuncy	Marks	Freqency
0-10	3	0-10	5
20-20	9	10-20	19
20-30	17	20-30	15
30-40	12	30-40	10
40-50	9	40-50	1

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

The length of 40 leaves of a plant are measured a correct one millimeter, and the obtained data is represented in the following table:

Length (in mm)	Number of leaves
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-171	4
172-180	2

(i) Draw a histogram to represent the given data.
(ii) Is there any suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the Indian society is given below:

Section	Number of girls per thousand boys
Scheduled Caste (SC)	940
Scheduled Tribe (ST)	970
Non SC/ST	920
Backward districts	950
Non-backward districts	920
Rural	930
Urban	910

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusion can be arrived at from the graph.

Generic 4

3 x 4 = 12

10.

The runs scored by two teams A and B on the first 42 balls in a cricket match are given below. Draw the frequency polygon on the same graph paper.

Number of balls	Team A	Team B
0-6	2	5
6-12	1	6
12-18	8	2
18-24	9	10
24-30	4	5
30-36	5	6
36-42	6	3

11.

Draw a histogram representing the following frequency distribution:

Marks	No. of students
0-10	3
10-20	5
20-30	8
30-40	10
40-50	7
50-60	2

12.

The following data gives the number (in thousands) of applicants registered with an Employment Exchange during 2005-2010.

Year	No.of applications registered (in thousands)
2005	19
2006	21
2007	23
2008	30
2009	32
2010	36

Construct a bar graph to represent the above data.

Multiple Choice Question

5 x 1 = 5

13.

The width of the class interval 70.5 - 75.5 is

(a)

(b)

2.5

(c)

0.5

(d)

10.

14.

In the distribution, the frequency of the class 0 - 5 is
0,3,2,5,8,10,13,5,6,6,14,0.

(a)

(b)

(c)

(d)

15.

Class mark =

(a)

\(\frac {lower \ limit + upper \ limit}{2}\)

(b)

lower limit + upper limit

(c)

upper limit - lower limit

(d)

\(\frac {lower \ limit - upper \ limit}{2}\)

16.

When the information is gathered from a source which already had the information stored, the data obtained is called

(a)

Primary data

(b)

Secondary data

(c)

Useless data

(d)

fictitious data

17.

Statistics is branch of

(a)

Mathematics

(b)

Physics

(c)

Chemistry

(d)

Psychology

Generic 5

2 x 5 = 10

18.

The % of marks obtained by students in the annual examination of a class in mathematics are given below:

Percentage of marks	No. of students
0-10	8
10-30	32
30-45	18
45-50	10

(i) How many students get less than 30% of marks?
(ii) Represent the data by histogram.
(iii) Which value is depicted by a student Ram obtaining the highest marks in the interval 45-50?

19.

Survey on the playing children of various age group is:

Age(in yrs)	No. of Children
1-2	5
2-3	3
3-5	6
5-7	12
7-10	9
10-15	10
15-17	4

Draw the histogram of above data

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Answers Key:

Generic 2

4 x 2 = 8

43,43

O	6
A	12
B	8
AB	4

(i) 15
(ii) 30-35
(iii) 47.5

Generic 3

5 x 3 = 15

The given data is
14,25,14,28,18,17,18,14,23,22,14,18
Arranging the data in ascending order, we have
14,14,14,14,17,18,18,18,22,23,25,28
Here, 14 occurs most frequently (4 times)
\(\therefore\) Mode = 14.

(i) Mean
\(Mean = \frac { Sum\ of\ all\ the\ observations }{ Total\ number\ of\ observations } \)
\(=\frac {41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}{15}\)
\(=\frac {822}{15}=54.8\)
(ii) Median
Arranging the given data in descending order, we have
98,96,62,54,52,52,48,46,42,41,40,40,39
Number of observations (n) = 15, which is odd.
\(\therefore\) Median \(=\left(\frac{n+1}{2}\right)^{th}{2}\) observation.
\(={ \left( \frac {15+1 }{ 2 } \right) }^{ th }\) observation
= 8^th observation = 52
(iii) Mode
Arranging the data in descending order, we have
98,96,62,60,54,52,52,52,48,46,42,41,40,39
Here, 52 occurs most frequently (3 times)
\(\therefore\) Mode = 52.

Modified Tables
For Section A

Marks	Class Marks	Freqeuncy
0-10	5	3
10-20	15	9
20-30	25	17
30-40	35	12
40-50	45	9

For Section B

Marks	Class Marks	Freqeuncy
0-10	5	5
10-20	15	19
20-30	25	15
30-40	35	10
40-50	45	1

Modified Continues Distribution

Length (in mm)	Number of leaves
117.5-126.5	3
126.5-135.5	5
135.5-144.5	9
144.5-153.5	12
153.5-162.5	5
162.5-171.5	4
171.5-180.5	2

(ii) Frequency Polygon.
(iii) No, because the maximum number of leaves have their lengths lying in the original interval 145-153 (or modified interval 144.5-153.5).

(ii) The two conclusions we can arrive at from the graph are as follows:
(a) The numbers of girls to the nearest ten per thousand boys is maximum in Scheduled Tribe section of the society and minimum in Urban section of the society.
(b) The number of girls to the nearest ten per thousand boys is the same for 'Non Sc/ST' and 'Non-backward Districts' sections of the society.

Generic 4

3 x 4 = 12

10.

11.

12.

Multiple Choice Question

5 x 1 = 5

13.

Width = 75.5 - 70.5 = 5.

14.

The item values included in 0 - 5 are 0,3,2,0.

15.

Formula

16.

Definition of a secondary data

17.

(a)
Mathematics

Generic 5

2 x 5 = 10

18.

(i) Required number of students = 8 + 32 = 40
(ii) Here, We notice that classes are continuous but class-size is not the same for all the classes. We notice minimum class-size is of class 45-50, i.e., 5. We will first find proportionate length of rectangle (adjusted frequency) for each class.
Length of rectangle (adjusted frequency) =\(\frac { Frequency\ of\ Class }{ Width\ of\ class } \times Minimum\ class-size\)

Marks (C.I.)	Number of students(f)	Width of class (Clss-size)	Length of rectangle
0-10	8	10	\(\frac{8}{10}\)x 5 = 4
10-30	32	20	\(\frac{32}{20}\) x 5 = 8
30-45	18	15	\(\frac{18}{15}\) x 5 = 6
45-50	10	5	\(\frac{10}{5}\) x 5 = 10

Now, we construct rectangles with respective class-intervals as widths and adjusted frequencies as heights.
Histogram representing marks obtained by students in unit test of Mathematics.

(iii) Hardwork and Dilligence.

19.

Age(in years)	No. of children	Width of class	Length of rectangle
1-2	5	1	\(\frac{5}{1}\)x1=5
2-3	3	1	\(\frac{3}{1}\)x1=3
3-5	6	2	\(\frac{6}{2}\)x1=3
5-7	12	2	\(\frac{12}{2}\)x1=6
7-10	9	3	\(\frac{9}{3}\)x1=3
10-15	10	5	\(\frac{10}{5}\)x1=2
15-17	4	2	\(\frac{4}{2}\)x1=2