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In the world of Mathematics, there are famous sayings: “Statistics: the only science that enables different experts using the same figures to draw different conclusions” and “Probability is not about certainty; it’s about possibility.” In simple terms, statistics help us represent large amounts of data using tables, graphs, and numbers. On the other hand, probability makes sense in terms of the likelihood of an event happening or not. In Chapter 14 Maths Exemplar Problems Class 10 Solutions, we will learn about various graphical representations of data, including the mean, median, and mode, as well as different types of probability questions.
Class 9th maths NCERT exemplar includes problems that are more challenging than the regular textbook exercises and ideal for higher classes and competitive exams. The main purpose of this NCERT exemplar class 10 Maths solutions is to make all the concepts crystal clear to students so that they can solve different kinds of problems on their own. The 2025-26 CBSE syllabus has been followed in these solutions and prepared by Careers360 experts having multiple years of experience in this field. Students can also check the NCERT books for Class 9 Maths to practice and gain knowledge.
Exercise: 14.1 Total Questions: 30 Page number: 131-136 |
Question:1
The class mark of the class 90-120 is :
Question:3
Answer: BQuestion:4
Answer: CQuestion:5
Answer: BQuestion:6
Answer: BQuestion:7
In the class intervals 10-20, 20-30, the number 20 is included in :
(A) 10-20
(B) 20-30
(C) both the intervals
(D) none of these intervals
Question:8
A grouped frequency table with class intervals of equal sizes using 250-270 (270 not included in this interval) as one of the class intervals is constructed for the following data :
The frequency of the class 310-330 is:
Question:9
A grouped frequency distribution table with classes of equal sizes using 63-72 (72 included) as one of the classes is constructed for the following data :
The number of classes in the distribution will be :
Question:10
To draw a histogram to represent the following frequency distribution :
Class interval | |||||
Frequency |
Question:11
Question:12
Answer:
In the given data the mean of the observations x, x + 3, x + 5, x + 7, x + 10 is given as 9Question:14
If each observation of the data is increased by 5, then their mean
(A) remains the same
(B) becomes 5 times the original mean
(C) is decreased by 5
(D) is increased by 5
Question:15
Let
If
Question:16
If
Question:17
Answer: CQuestion:18
The mean of 100 observations is 50. If one of the observations, which was 50, is replaced by 150, the resulting mean will be :
(A) 50.5
(B) 51
(C) 51.5
(D) 52
Question:19
There are 50 numbers. Each number is subtracted from 53, and the mean of the numbers so obtained is found to be -3.5. The mean of the given numbers is :
(A) 46.5
(B) 49.5
(C) 53.5
(D) 56.5
Question:20
Answer: BQuestion:21
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is
Question:22
For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abscissae are respectively :
(A) upper limits of the classes
(B) lower limits of the classes
(C) class marks of the classes
(D) upper limits of preceding classes
Class interval | Class marks (x-coordinate) | Frequency (y-coordinate) |
10-20 | 15 | 7 |
20-30 | 25 | 8 |
30-40 | 35 | 9 |
Question:23
Median of the following numbers: 4, 4, 5, 7, 6, 7, 7, 12, 3 is
Question:24
Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is
(A) 14
(B) 15
(C) 16
(D) 17
Question:25
Answer : DQuestion:26
Answer: CQuestion:27
In a medical examination of students of a class, the following blood groups are recorded:
Blood Group | A | AB | B | O |
Number of students | 10 | 13 | 12 | 5 |
Number of students with blood group B =12
Total number of students =10+13+12+5
Required probability
Therefore, option (B) is correct.
Question:28
Two coins are tossed 1000 times, and the outcomes are recorded as below :
Number of heads | 2 | 1 | 0 |
Frequency | 200 | 550 | 250 |
Question:29
Life time (in hours) | 300 | 500 | 700 | 900 | 1100 |
Frequency | 10 | 12 | 23 | 25 | 10 |
Question:30
Life time (in hours) | 300 | 500 | 700 | 900 | 1100 |
Frequency | 10 | 12 | 23 | 25 | 10 |
Exercise: 14.2 Total Questions: 10 Page number: 136-138 |
Question:1
Marks | 0-20 | 20-40 | 40-60 | 60-100 |
Number of Students | 10 | 15 | 20 | 25 |
Marks | 0-20 | 20-40 | 40-60 | 60-100 |
Number of Students | 10 | 15 | 20 | 25 |
Class interval (x-axis) | Frequency (y-axis) |
0-20 | 10 |
20-40 | 15 |
40-60 | 20 |
60-100 | 25 |
Question:2
In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded:
Which ‘average’ will be a good representative of the above data and why?
Question:3
Answer: The child has not arranged the data in ascending order before finding the medianQuestion:4
A football player scored the following number of goals in the 10 matches: 1, 3, 2, 5, 8, 6, 1, 4, 7, 9
Since the number of matches is 10 (an even number), therefore, the median
Is it the correct answer, and why?
Answer:
Answer : [No, as the data is not arranged in ascending order before finding the middle terms]
Given terms: 1, 3, 2, 5, 8, 6, 1, 4, 7, 9
To calculate the median, arrange the given data in ascending order and then find the middle term. This middle term is called the median.
Firstly, we will arrange the data in ascending order as:
Here, the total number of observations, n=10 which is even.
In case of an even number of terms:
Hence, the median is 4.5.
Question:5
Answer: NoQuestion:6
The class marks of a continuous distribution are :
Is it correct to say that the last interval will be 1.55 - 1.73? Justify your answer.
Class-marks | Difference |
1.14-1.04 | 0.1 |
1.24-1.14 | 0.1 |
1.34-1.24 | 0.1 |
1.44-1.34 | 0.1 |
1.54-1.44 | 0.1 |
1.55-1.73 | 0.8 |
Question:7
Number of hours | 0-5 | 5-10 | 10-15 | 15-20 |
Frequency | 8 | 16 | 4 | 2 |
Question:8
Can the experimental probability of an event be a negative number? If not, why?
Answer: NoQuestion:9
Can the experimental probability of an event be greater than 1? Justify your answer.
Answer: NoQuestion:10
Answer: NoExercise: 14.3 Total Questions: 20 Page number: 140-145 |
Question:1
The blood groups 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 frequency distribution table for the data.
Answer:
Given data :Blood group | Frequency distribution table |
A | 12 |
B | 8 |
AB | 4 |
O | 6 |
Total | 30 |
Question:2
Answer:
We have to make a frequency distribution of the digits 0 to 9 after the decimal point.Digit | Frequency |
0 | 1 |
1 | 2 |
2 | 5 |
3 | 6 |
4 | 3 |
5 | 4 |
6 | 3 |
7 | 2 |
8 | 5 |
9 | 4 |
Total | 35 |
Question:3
The scores (out of 100) obtained by 33 students in a mathematics test are as follows:
69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84, 66, 64, 71, 64, 66,
Represent this data in the form of a frequency distribution.
Answer:
Given data :
The data can be arranged in ascending order as:
Frequency distribution table:
Question:4
Prepare a continuous grouped frequency distribution from the following data:
Mid-Point | Frequency |
5 | 4 |
15 | 8 |
25 | 13 |
35 | 12 |
45 | 6 |
Also, find the size of class intervals.
Answer:
Question:5
Convert the given frequency distribution into a continuous grouped frequency distribution:
Class interval | Frequency |
150-153 | 7 |
154-157 | 7 |
158-161 | 15 |
162-165 | 10 |
166-169 | 5 |
170-173 | 6 |
Answer:
Given classes are :Class interval | Frequency |
149.5-153-5 | 7 |
153.5-157.5 | 7 |
157.5-161.5 | 15 |
161.5-165.5 | 10 |
165.5-169.5 | 5 |
169.5-173.5 | 6 |
Question:6
The expenditure of a family on different heads in a month is given below:
Head | Food | Education | Clothing | House Rent | Others | Savings |
Expenditure (in Rs) | 4000 | 2500 | 1000 | 3500 | 2500 | 1500 |
Answer:
Here, we will draw a bar graph to represent the expenditure of a family for different heads in a month as follows:Question:7
Elementary education | 240 |
Secondary Education | 120 |
University Education | 190 |
Teacher's Training | 20 |
Social Education | 10 |
Other Educational Programmes | 115 |
Cultural programmes | 25 |
Technical Education | 125 |
Answer:
Expenditure on Education of a country during a five year period (2002-2006), in crores of rupees, is given below:Elementry education | 240 |
Secondary Education | 120 |
University Education | 190 |
Teacher's Training | 20 |
Social Education | 10 |
Other Educational Programmes | 115 |
Cultural programmes | 25 |
Technical Education | 125 |
Question:8
Letters | a | e | i | o | r | t | u |
Frequency | 75 | 125 | 80 | 70 | 80 | 95 | 75 |
Answer:
We will draw the graph with letters (a, e, i, o, r, t, u) as follows:Question:9
If the mean of the following data is 20.2, find the value of p:
x | 10 | 15 | 20 | 25 | 30 |
f | 6 | 8 | p | 10 | 6 |
10 | 6 | 60 |
15 | 8 | 120 |
20 | p | 20 p |
25 | 10 | 250 |
30 | 6 | 180 |
Question:10
Obtain the meaning of the following distribution:
Frequency | Variable |
4 | 4 |
8 | 6 |
14 | 8 |
11 | 10 |
3 | 12 |
4 | 4 | 16 |
6 | 8 | 48 |
8 | 14 | 112 |
10 | 11 | 110 |
12 | 3 | 36 |
Question:11
Answer: 72.2Hence, the mean of the whole class is 72.2.
Question:12
Answer :Question:13
Answer: 20Question:14
The points scored by a basketball team in a series of matches are as follows:
Find the median and mode for the data.
Question:15
Answer:
Based on the given bar graph :Class-Interval | Frequency |
150-200 | 50 |
200-250 | 30 |
250-300 | 35 |
300-350 | 20 |
350-400 | 10 |
Total workers | 145 |
Question:16
Monthly income (in Rs) | Number of Televisions/household | ||||
0 | 1 | 2 | Above 2 | ||
<10000 | 20 | 80 | 10 | 0 | |
10000-14999 | 10 | 240 | 60 | 0 | |
15000-19999 | 0 | 380 | 120 | 30 | |
20000-24999 | 0 | 520 | 370 | 80 | |
25000 and above | 0 | 1100 | 760 | 220 |
Answer:
Here, total events =4000Question:17
Sum | Frequency |
2 | 14 |
3 | 30 |
4 | 42 |
5 | 55 |
6 | 72 |
7 | 75 |
8 | 70 |
9 | 53 |
10 | 46 |
11 | 28 |
12 | 15 |
Answer:
Question:18
Bulbs are packed in cartons, each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs, and the results are given in the following table:
One carton was selected at random. What is the probability that it has
(i) No defective bulb?
(ii) defective bulbs from 2 to 6?
(iii) defective bulbs less than 4?
Answer:
Question:19
Number of defective parts | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
Days | 50 | 32 | 22 | 18 | 12 | 12 | 10 | 10 | 10 | 8 | 6 | 6 | 2 | 2 |
Answer:
Question:20
A recent survey found that the ages of workers in a factory are distributed as follows:
Age (in years) | 20-29 | 30-39 | 40-49 | 50-59 | 60 and above |
Number of workers | 38 | 27 | 86 | 46 | 3 |
Answer:
(iv) p(under 60 but over 39 years) = p(person having age 40 to 49 years) + p (person having age 50 to 59 years)
Exercise: 14.4 Total Questions: 12 Page number: 147-149 |
Question:1
The following are the marks (out of 100) of 60 students in mathematics.
Construct a grouped frequency distribution table with width 10 of each class starting from 0 - 9.
Answer:
Step 1: Arrange these numbers in ascending order.
Step 2: Make the frequency distribution table as follows:
The class interval of (0-9), (10-19), etc., are given.
So, we can write the class interval and the corresponding frequency.
Class interval | Frequency |
0-9 | 4 |
10-19 | 7 |
20-29 | 5 |
30-39 | 10 |
40-49 | 5 |
50-59 | 8 |
60-69 | 5 |
70-79 | 8 |
80-89 | 5 |
90-99 | 3 |
Total | 60 |
Question:2
The following are the marks (out of 100) of 60 students in mathematics.
Construct a grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 - 20 (20 not included).
Answer:
Step 1: Arrange these numbers in ascending order.Class interval | Frequency |
0-10 | 4 |
10-20 | 7 |
20-30 | 5 |
30-40 | 10 |
40-50 | 5 |
50-60 | 8 |
60-70 | 5 |
70-80 | 8 |
80-90 | 5 |
90-100 | 3 |
Total | 60 |
Question:3
Draw a histogram of the following distribution :
Heights (in cm) | Number of students |
150-153 | 7 |
153-156 | 8 |
156-159 | 14 |
159-162 | 10 |
162-165 | 6 |
165-168 | 5 |
Answer:
To draw the histogram, we have to plot the frequency, i.e., number of students on the y-axis and class interval, i.e., heights on the x-axis. We can construct the histogram as follows:Question:4
Draw a histogram to represent the following grouped frequency distribution :
Ages (in years) | Number of teachers |
20-24 | 10 |
25-29 | 28 |
30-34 | 32 |
35-39 | 48 |
40-44 | 50 |
45-49 | 35 |
50-54 | 12 |
Answer:
We can see that the intervals are 20-24, 25-29, 30-34....etcAges | No. of teachers |
19.5-24.5 | 10 |
24.5-29.5 | 28 |
29.5-34.5 | 32 |
34.5-39.5 | 48 |
39.5-44.5 | 50 |
44.5-49.5 | 35 |
49.5-54.5 | 12 |
Question:5
Length (in mm) | Number of leaves |
118-126 | 8 |
127-135 | 10 |
136-144 | 12 |
145-153 | 17 |
154-162 | 7 |
163-171 | 5 |
172-180 | 3 |
Answer:
We can see that the intervals are 118-126, 127-135, 136-144...etcLength (in mm) | Number of leaves |
117.5-126.5 | 8 |
126.5-135.5 | 10 |
135.5-144.5 | 12 |
144.5-153.5 | 17 |
153.5-162.5 | 7 |
162.5-171.5 | 5 |
171.5-180.5 | 3 |
Question:6
The marks obtained (out of 100) by a class of 80 students are given below :
Marks | Number of students |
10-20 | 6 |
20-30 | 17 |
30-50 | 15 |
50-70 | 16 |
70-100 | 26 |
Answer:
To draw the histogram, we have to plot the frequency, i.e., number of students on the y-axis and class interval, i.e., marks on the x-axis. We can construct the histogram as follows:Question:7
Class interval (km/h) | Frequency |
30-40 | 3 |
40-50 | 6 |
50-60 | 25 |
60-70 | 65 |
70-80 | 50 |
80-90 | 28 |
90-100 | 14 |
Answer:
To draw the histogram, we have to plot the frequency on the y-axis and the class interval on the x-axis. We can construct the histogram as follows:Question:8
Class interval (km/h) | Frequency |
30-40 | 3 |
40-50 | 6 |
50-60 | 25 |
60-70 | 65 |
70-80 | 50 |
80-90 | 28 |
90-100 | 14 |
Answer:
A frequency polygon is a graph constructed by using lines to join the midpoints of each interval.Question:9
Section A | Section B | ||
Marks | Frequency | Marks | Frequency |
0-15 | 5 | 0-15 | 3 |
15-30 | 12 | 15-30 | 16 |
30-45 | 28 | 30-45 | 25 |
45-60 | 30 | 45-60 | 27 |
60-75 | 35 | 60-75 | 40 |
75-90 | 13 | 75-90 | 10 |
Answer:
Marks | Class marks | Frequency A | Frequency B |
0-15 | 5 | 3 | |
15-30 | 12 | 16 | |
30-45 | 28 | 25 | |
45-60 | 30 | 27 | |
60-75 | 35 | 40 | |
75-90 | 13 | 10 |
Question:10
The mean of the following distribution is 50.
Find the value of a and hence the frequencies of 30 and 70.Answer:
10 | 17 | 170 |
30 | ||
50 | 32 | 1600 |
70 | ||
90 | 19 | |
Total |
Question:10
The mean of the following distribution is 50.
x | f |
10 | |
30 | |
50 | |
70 | |
90 |
Answer:
10 | 17 | 170 |
30 | ||
50 | 32 | 1600 |
70 | ||
90 | 19 | |
Total |
Question:11
Answer : [ 2:1 ]Question:12
Answer:
Answer: The mean is 75.88, mode is 85, median is 77Mode is the value that occurs the most number of times in a given set of values
So, 85 is the mode, and its frequency is 4 times.
To calculate the median, arrange the given data in ascending order and then find the middle term. This middle term is called the median.
The data in ascending order is:
Number of terms, n=25
13th term is 77
Hence, the median is 77.
Students can also check the NCERT Exemplar solutions of other subjects using the following links.
Class 9 Maths NCERT exemplar solutions chapter 14 Statistics and Probability provides adequate practice and information on this chapter in a student-friendly process flow that can be further applied in higher classes as well as in exams like NTSE, JEE, Olympiads, etc. Here are some more points on why students should check these solutions.
NCERT textbook solutions of other subjects have also been provided in the links below.
Notes can be used during revision time to recall important concepts and formulas. The following links will lead students to well-structured notes that they can use to achieve excellence.
Students can use the following links to find the 2025-26 CBSE syllabus and reference books to practice.
No, the possibility of occurring or not occurring may have different methods. Therefore, we can say occurring or non-occurring are not equally likely. If two events are not equally likely their probability will not be the same.
Mean, median, and mode of any data represent the central tendency of the data.
Mode represents the most favourable data outcome.
Mean represent the average value of the data.
Median represents the middle value, if the data is arranged in decreasing or increasing order.
When the occurrence of any event cannot be denied, the event is called a sure event. For example, the sun will rise in the east can be seen as a sure event. The probability of a sure event is one.
The probability of any event cannot be more than one. The maximum probability is 1 for sure events. The minimum probability is 0 for impossible events
On the basis of analysis of large data, we estimate the occurrence of any event this analysis is called statistical probability. Most of the recent scientific researches are based on statistical probability
The chapter on Statistics and Probability is a very important chapter from the exam’s perspective as it accounts for 10-12% marks of the final paper. NCERT exemplar Class 9 Maths solutions chapter 14 provides sufficient learning content to the students to develop a better understanding and score well in the exam.
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