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Published on: 29/10/2025

Question Set B

CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365

Download CBSE Class 9th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 9th Standard CBSE Mathematics

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Std: 9th Standard CBSE - Mathematics

chapter: Statistics - Sample Question Papers

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Questions:

Generic 4

2 x 4 = 8

The following table gives the life times of 400 neon lamps:

Lifetime (in years)	Number of Lamps
300-400	14
400-500	56
500-600	60
600-700	86
700-800	74
800-900	62
900-1000	48

(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life time of more than 700 hours?

The class marks of a frequency distribution are 104, 114, 124, 134, 144, 154, 164. Find the class size and class intervals.

Generic 2

3 x 2 = 6

The mean of 100 observations is 60. If one observation of 50 is replaced by 110, then what will be the new mean?

5 people were asking about the time in a week they spend in doing social work in their community. They said 10,7,13,20 and 15 hours, respectively. Find the mean (or average) time in a week denoted by them social work

The marks obtained by 40 students of class IX in an examination are given below:

18	16	16	12	3	15	21	7
8	12	23	9	5	20	16	3
12	5	2	7	13	24	13	18
6	23	10	6	21	1	18	17
8	2	20	5	13	7	23	16

Present the data in the form of a frequency distribution using equal class-size, one such class being 10-15 (15 not included.)

Generic 3

5 x 3 = 15

Thirty children spent about the number of hours they watched TV programs in the previous week. The result was as follow:

1	2	10	10	8	4
10	2	5	8	9	8
3	4	5	6	1	4
6	8	2	5	8	6
3	3	9	10	4	8

(i) Prepare a frequency table for the data given.
(ii) Find the mode of the data.

A family with a monthly income of Rs. 20,000 had planned the following expenditure per month under various heads.

Heads	Expenditure (in thousand rupees)
Grocery	04
Rent	05
Education	05
Medicine	02
Fuel	02
Entertainment	01
Miscellaneous	01

Draw a bar graph for the data above

For a particular year, following is the distribution of ages (in hours) of primary school teachers in a particular state.

Age (in years)	No. of teachers
Less than 20	11
21-25	32
26-30	51
31-35	49
36-40	27
41-45	6
46-50	4

1. Determine the class limits of the fourth class.
2. What is the class size?
3. Construct a cumulative frequency table.

Represent the following data by means of histogram.

Weekly wages (in Rs)	No. of workers
1000-1100	5
1100-1200	7
1200-1350	6
1350-1450	2
1450-1700	10
1700-1900	6

10.

A random survey of the number of children of various age groups playing in a park was found as follows:

Age (in years)	Number of children
1-2	5
2-3	3
3-5	6
5-7	12
7-10	9
10-15	10
15-17	4

Draw a histogram to represent the data above.

Multiple Choice Question

10 x 1 = 10

11.

Median of given data is: 144,145,147,148,149,150,152,155,160

(a)

148

(b)

149

(c)

150

(d)

160

12.

If the median of the following data arranged in ascending order is 18, then the value of x is 8 11 12 16 16+x 20 25 30

(a)

(b)

(c)

(d)

13.

If the mean of 5,10,15,p,20,35,40 is 21. Then the value of p is

(a)

(b)

(c)

(d)

14.

Find the mean of all possible factors of 10.

(a)

(b)

4.5

(c)

(d)

15.

Two consecutive class marks of a distribution are 52 and 57. Then the class size is:

(a)

2.5

(b)

(c)

54.5

(d)

109

16.

Class mark of a class interval 15 - 25 is:

(a)

(b)

(c)

(d)

17.

The upper limit of the class 36 - 40 is

(a)

(b)

(c)

(d)

41.

18.

The lower limit of the class 31-35 is

(a)

(b)

(c)

(d)

19.

Facts or information collected with a definite purpose are called:

(a)

Median

(b)

Mode

(c)

Data

(d)

Histogram

20.

The word 'Latum' is a

(a)

Latin word

(b)

German word

(c)

English word

(d)

Sanskrit word

1 Marks

2 x 1 = 2

21.

The points scored by a basketball team in a series of matches are as follows: 17,2,7,17,25,514,18,10. Find range.

22.

Find the mean of first six odd numbers.

Generic 5

1 x 5 = 5

23.

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?

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Answers Key:

Generic 4

2 x 4 = 8

Lifetime (in yours)	Class Marks	Number of lapms (frequency)
300-400	350	14
400-500	450	56
500-600	550	60
600-700	650	86
700-800	750	74
800-900	850	62
900-1000	950	48

(ii) 74 + 62 + 48 = 184 have a life time of more than 700 hours

Class size = 114 -104 = 10
\(\frac {10}{2}=5\)
The class intervals are
104-5___104+5, i.e., 99-109;
114-5___ 114+5, i.e, 109-119;
124-5___ 124+5, i.e., 119-129;
134-5___ 134+5, i.e., 129-139;
144-5___ 144+5, i.e., 139-149;
154-5___ 154+5, i.e., 149-159;
164-5___ 159-169.

Generic 2

3 x 2 = 6

60.6

13 hours.

0-5	5
5-10	11
10-15	7
15-20	9
20-25	8

Generic 3

5 x 3 = 15

(i) Frequency Table:

No. of hours	Tally Marks	No.of students
1	II	2
2	III	3
3	III	3
4	IIII	4
5	III	3
6	III	3
8	III I	6
9	II	2
10	IIII	4
Total		30

(ii) Mode = 8, as 8 occurs maximum number of times i.e., 6 times.

1. 30.5-35.5;
2.1;
3.

Less than 20	11
Less than 25	43
Less than 30	94
Less than 35	143
Less than 40	170
Less than 45	176
Less than 50	180

Hint

Weekly wages (in Rs)	No. of workers (frequency)	Adjusted frequency
1000-1100	5	\(\frac {100}{100}\times 5\)
1100-120	7	\(\frac {100}{100}\times 7\)
12001350	6	\(\frac {100}{150}\times 6\)
1350-1450	2	\(\frac {100}{100}\times 2\)
1450-1700	10	\(\frac {100}{250}\times 10\)
1700-1900	6	\(\frac {100}{200}\times 6\)

10.

Modified Table
[Minimum class-size = 1]

Age (in years)	Number of children (frequency)	Width of the class	Length of the rectangle
1-2	5	1	\(\frac {5}{1}\times 1 = 5\)
2-3	3	1	\(\frac {3}{1}\times 1 = 3\)
3-5	6	2	\(\frac {6}{2}\times 1 = 3\)

Age (in years)	Number of children (frequency)	Width of the class	Length of the rectangle
5-7	12	2	\(\frac {12}{2}\times 1 = 6\)
7-10	9	3	\(\frac {9}{3}\times 1 = 3\)
10-15	10	5	\(\frac {10}{5}\times 1 = 2\)
15-17	4	2	\(\frac {4}{2}\times 1 = 2\)

Multiple Choice Question

10 x 1 = 10

11.

Data are in ascending order
n = 9(odd)
Median = 9 + 1/2 th observation

12.

(d)
4

13.

\(\frac{5+10+15+p+20+35+40}{7}=21\)
\(\Rightarrow\) p = 22.

14.

All possible factors of 10 are 1,2,5 and 10. \(\overset{-}{x}=\frac{1+2+5+10}{4}=4.5.\)

15.

Class size = 57 - 52 = 5

16.

Class mark \(= \frac {15+25}{2}=20\)

17.

18.

Sixth class is 25 - 30.

19.

Definition of data.

20.

(a)
Latin word

1 Marks

2 x 1 = 2

21.

()
Range = highest point-lowest point
= 27 - 2 = 25

22.

()
Mean = \(\frac{1+3+5+7+9+11}{6}\)=\(\frac{36}{6}\)
= 6

Generic 5

1 x 5 = 5

23.

(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.