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CBSE 9th Standard Mathematics Statistics Important Questions And Answers Study Material - QB365 Set C

Published on: 29/10/2025

Question Set C

CBSE 9th Standard Mathematics Statistics Important Questions And Answers 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 - Important Questions And Answers

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Questions:

Generic 2

4 x 2 = 8

If the mean of the data \(x_1,x_2,x_3,......x_n\) is 72, find the mean of the data \(3x_1,3x_2,...3x_n\)

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.

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 out of 75 by 30 students of a class in an examination are given below:
42,21,50,37,42,37,38,42,49,52,38,53,57,47,29,59,61,33,17,17,39,44,42,39,14,7,27,19,54,51
Prepare a frequency distribution table in which the size of class intervals is the same and one class intervalis 0-10.

Generic 3

4 x 3 = 12

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29,32,48,50,x,x+2,72,78,84,95

The following number of goals were scored by a term in a series of 10 matches:
2,3,4,5,0,1,3,3,4,3
Find the mean, median and mode of these scores.

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.

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

Political Party	A	B	C	D	E	F
Seat won	75	55	37	29	10	37

(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?

Generic 4

5 x 4 = 20

Draw a frequency polygon for the data given below, without drawing a histogram.

Classes	Frequency
150 -160	5
160 -170	15
170 -180	20
180 -190	25
190 - 200	15
200 - 210	5

10.

Consider the marks out of 100, obtained by 50 students of a class in a test, given as below.

Marks	0-20	20-40	40-60	60-80	80-100
No. of students	15	10	10	11	4

Draw a frequency polygon representing the data

11.

The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

12.

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

13.

The marks scored by 750 students in examination are given in the form a frequency distribution table.

Marks	No. of students
600-640	16
640-680	45
680-720	156
720-760	284
760-800	172
800-840	59
840-880	18

Draw a histogram to represent the above data.

Multiple Choice Question

5 x 1 = 5

14.

The upper limit of the class 36 - 40 is

(a)

(b)

(c)

(d)

41.

15.

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

16.

'Number of absentees in each day in your class for a month' form

(a)

Useless data

(b)

Fictitious data

(c)

Secondary data

(d)

Primary data

17.

Statistics is branch of

(a)

Mathematics

(b)

Physics

(c)

Chemistry

(d)

Psychology

18.

The word 'Latum' is a

(a)

Latin word

(b)

German word

(c)

English word

(d)

Sanskrit word

1 Marks

5 x 1 = 5

19.

The class-mark of the class 130-150 is

20.

The range of the data is: 25,18,20,22,16,6,17,12,30,32,10,19,8,11,20 is:

21.

Find the range of the data: 22,25,20,32,36,28,40,45,35,38

22.

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.

23.

Find the mode of the numbers: 14,14,15,27,26,27,27,22,13

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Answers Key:

Generic 2

4 x 2 = 8

216

43,43

13 hours.

Class	Frequency
0-10	1
10-20	4
20-30	3
30-40	7
40-50	7
50-60	7
60-70	1
Total	30

Generic 3

4 x 3 = 12

Number of observations (n) = 10, which is even.
\(\therefore\) Median
\(=\frac { { \left( \frac { n }{ 2 } \right) }^{ th }observation+{ \left( \frac { n }{ 2 } +1 \right) }^{ th }observation }{ 2 } \)
\(=\frac { { \left( \frac { 10 }{ 2 } \right) }^{ th }observation+{ \left( \frac { 10 }{ 2 } +1 \right) }^{ th }observation }{ 2 } \)
\(=\frac { { 5 }^{ th }observation+{ 6 }^{ th }observation }{ 2 } \)
\(=\frac { x+\left( x+2 \right) }{ 2 } =x+1\)
According to the question,
x + 1 = 63
\(\Rightarrow\) x = 63 - 1
\(\Rightarrow\) x = 62
Hence, the value of x is 62.

(i) Mean
\(Mean = \frac { Sum\ of\ all\ the\ observations }{ Total\ number\ of\ observations } \)
\(=\frac { 2+3+4+5+0+1+3+3+4+3 }{ 10 } \)
\(=\frac { 28 }{ 10 } =2.8\)
(ii) Median
Arranging the given data in ascending order, we have
0,1,2,3,3,3,3,4,4,5
Number of observations (n) = 10, which is even.
\(\therefore\) Median
\(= \frac {\left (\frac{n}{2}\right)^{th} observation + \left(\frac {n}{2}+1\right)^{th} observation}{2}\)
\(= \frac {\left (\frac{10}{2}\right)^{th} observation + \left(\frac {10}{2}+1\right)^{th} observation}{2}\)
\(\frac {{5}^{th} observation+{6}^{th}observation}{2}\)
\(\frac{3+3}{2}=\frac{6}{2}=3\)
(iii) Mode
Arranging the given data in ascending order, we have
0,1,2,3,3,3,3,4,4,5
Here, 3 occurs most frequently (4 times)
\(\therefore\) Mode = 3.

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	\(\frac {4}{2}\times 1 = 2\)

(i)

(ii) Political party A won the maximum number of seats.

Generic 4

5 x 4 = 20

Frequency polygon is with class marks:

Class Marks	Frequency
155	5
165	15
175	20
185	25
195	15
205	5

Frequency polygon showing various frequency for the class intervals given

10.

Marks	No. of students
0-20	15
20-40	10
40-60	10
60-80	11
80-100	4

Frequency polygon graph is ABCDEFG

11.

\(\therefore\) Mean of 200 items = 50
\(\therefore\) Sum of items \(= 200 \times 50 = 10000\)
Corrected sum = 10000 - (92 + 8) + (192 + 88)
= 10180
\(\therefore\) Correct mean \(= \frac {10180}{200}=50.9\)

12.