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

Published on: 29/10/2025

Question Set E

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:

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.

The marks obtained by 40 students of class IX in an examination are given below:
12,8,18,8,6,16,12,5,
23,2,10,20,12,9,7,6,
5,3,5,13,21,13,15,20,
24,1,7,16,21,13,23,18,
7,3,18,17,16,16,23,12
Represent the data in the form of a freqency distribyuting using 15-20 (20 not included) as one of the class intervals.

Prepare a frequency table from the data follows:

Marks obtained	No. of students
More than or equal to 0	50
More than or equal to 20	48
More than or equal to 40	41
More than or equal to 60	30
More than or equal to 80	12

Consider the marks, out of 100, obtained by 51 students of a class in a test:

Marks	Number of students
0-10	5
10-20	10
20-30	4
30-40	6
40-50	7
50-60	3
60-70	2
70-80	2
80-90	3
90-100	9
Total	51

Draw a frequency polygon corresponding to this frequency distribution table.

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.

If the median of the data 12,24,30,35,37,40,3m,3m + 4,52,57,59,62,67,70 which is arranged in ascending order, is 47, find the value of m.

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

The mean of 10 numbers is 50. If one more number is ordered, then the mean is 50 itself. Find the added number.

10.

If the mean of the following data is 15, find p:

x	f
5	6
10	p
15	6
20	10
25	5

11.

Find the median of the squares of the first 8 natural numbers.

12.

Read the bar graph. Find the percentage of excess expenditure on wheat than pulses and ghee taken together.

13.

From the following observations:
0.03,0.05,1.04,0.08,0.05,1.03,0.03,0.04,0.07,0.05, 0.02, 1.00, 0.08
(i) Calculate the Mode
(ii) Calculate the Range

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Answers Key:

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

0-5	4
5-10	11
10-15	8
15-20	9
20-25	8

0-20	2
20-40	7
40-60	11
60-80	18
80 & Above	12

Let us first draw a histogram for this data and mark the mid-points of the tops of the rectangles as B, C, D, E, F, G, H, I, J, K, respectively. Here, the first class is 0-10. So, to find the class preceeding 0-10, we extend the horizontal axis in the negative direction and find the mid-point of the imaginary class-interval (–10) - 0. The first end point, i.e., B is joined to this mid-point with zero frequency on the negative direction of the horizontal axis. The point where this line segment meets the vertical axis is marked as A. Let L be the mid-point of the class succeeding the last class of the given data. Then OABCDEFGHIJKL is the frequency polygon, which is shown in Fig.

43,43

60.6

10.

11.

Ascending order of terms 1,4,9,16,25,36,49,64
no. of terms = 8(even)
Median = Mean of 4th and 5th terms
=\(\frac{16+25}{2}=\frac{41}{2}\) = 20.5

12.

Expenditure on pulses and ghee
= 10% + 20% = 30%
Expenditure on wheat = 35%
Excess expenditure on wheat = 35% - 30% = 5%

13.

Arranging the data in ascending order
0.02, 0.03, 0.03, 0.04, 0.05, 0.05, 0.05, 0.07, 0.08, 0.08, 1.00, 1.03, 1.04
Mode = 0.05
Range = 1.04 - 0.02 = 1.02.