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

Published on: 29/10/2025

Question Set D

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:

Give five examples of data that you can collect from your day-to-day life.

The mean of monthly salary of 12 employees of a firm is Rs.14,500. If one more person joins the firm who gets Rs.18,400 per month, than what will the mean monthly salary now.

A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):

S.No.	Causes	Female fatality rate (%)
1.	Reproductive health conditions	31.8
2.	Neuropstchiatric conditions	25.4
3.	Injuries	12.4
4.	Cardiovascular conditions	4.3
5.	Respiratory conditons	4.1
6.	Other causes	22.0

(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women's ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.

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?

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.

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.

The median of observations 11,12,14,18,x+2,x+4,30,32,35 and 41 arranged in ascending order is 24. Find x.

Find the mode and median of the following data: 15,3,7,27,17,5,14,8,9,12,24,27,7,27,30

The class marks of a distribution are 37, 42, 47, 52, 57. Determine the class size and the class limits of one last class mark.

10.

Statistics is branch of

(a)

Mathematics

(b)

Physics

(c)

Chemistry

(d)

Psychology

11.

'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

12.

Class mark =

(a)

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

(b)

lower limit + upper limit

(c)

upper limit - lower limit

(d)

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

13.

The range of the following frequency distribution is
2.7,2.7,2.8,2.1,2.4,3.2,2.1,3.1,2.8,3.2.

(a)

2.1

(b)

1.6

(c)

5.3

(d)

1.1

14.

Class mark of a class interval 15 - 25 is:

(a)

(b)

(c)

(d)

15.

The position average is

(a)

arithmetic mean

(b)

median

(c)

geometric mean

(d)

harmonic mean

16.

For what value of x, is the mode of the following data 9?
5,8,9,3,9,8,7,6,8,9,x,4

(a)

(b)

(c)

(d)

17.

If the mean of 10 observations is 15, then their algebraic sum is

(a)

1.5

(b)

(c)

(d)

150.

18.

A student got respectively 85,87 and 83 marks in Mathematics, Physics, and Chemistry. The mean of his mark is

(a)

(b)

(c)

(d)

85.5

19.

The mean 1,2,3,4,5x is

(a)

(b)

(c)

x + 2

(d)

5x + 1.

20.

Find the mean of first six odd numbers.

21.

The number of children in 10 families of a locality are: 2,4,3,4,2,0,3,5,1,6. Find the mean number of children per family.

22.

Mean of 15 observation is 23. If each observation is multiplied by 2, find new mean.

23.

For the given data: 11,15, 17, y+1, 19, y-2, 3; if the mean is 14, find the value of y.

24.

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

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Answers Key:

(i) Number of students
(ii) Number of fans un our school.
(iii) Electricity bills of our house for last two years.
(iv) Election results obtained from television or newspaper.
(v) Literacy rate figures obtained from Educational Survey.

Mean monthly salary of 12 employees = Rs.14,500
Sum of monthly salary of 12 employees
= 14,500 x 12
= Rs.1,74,000
ஃ Sum of monthly salary of 13 employees
= 1,74,000 + 18,400
= Rs.1,92,400
ஃ Mean of monthly salary of 13 employees
= \(\frac{1,92,400}{13}\) = Rs.14,800

(i)

(ii) Reproduce health conditions is the major cause of women's ill health and death worldwide.
(ii) Lack of proper diet, lack of advised exercises.

(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.

43,43

n = 10
Median = average of 5th and 6th observations
=\(\frac{(x+2)+(x+4)}{2}\)
⇒ 24 =\(\frac{2x+6}{2}\)
x = 21

Arranging the data in ascending order 3,5,7,7,8,9,12,14,15,17,24,27,27,27,30
Total number of observations = 15
Median \((\frac{15+1}{2})^{th}\) i.e., 8th observation =14
In the data 27 occurs most frequently (three times)
ஃ Mode = 27

Class size = 42 - 37 = 5
Lower limit of last class mark = 57-\(\frac{5}{2}\) = 54.5
Upper limit of last class mark = 57+\(\frac{5}{2}\) = 59.5

10.

(a)
Mathematics

11.

(a)
Useless data

12.

Formula

13.

Highest item value = 3.2
Lowest item value = 2.1
\(\therefore\) Range = 3.2 -2.1 = 1.1.

14.

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

15.

Median divides the whole distribution into two equal parts.

16.

17.

Requires sum \(= 10 \times 15 = 150.\)

18.

\(\overset{-}{x}=\frac {85+87+83}{3}=\frac{255}{3}=85.\)

19.

\(\overset{-}{x}=\frac{1+2+3+4+5x}{2}=x + 2.\)

20.

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

21.

()
Mean number of children per family =\(\frac{2+4+3+4+2+0+3+5+1+6}{10}=\frac{30}{10}\) = 3

22.

()
If each observation under consideration is multiplied by 2, then new mean in obtained by multiplying same quantity(i.e., 2) in old mean
ஃ New mean = 2 x old mean
= 2 x 23
= 46

23.