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NCERT Solutions for Exercise 14.3 Class 10 Maths Chapter 14 Statistics are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 202324. Class 10 Maths ex 14.3 introduces us to the concept of finding the median. In ninth grade, we learned about the median of grouped data. The median is a measure of central tendency that represents the value of the data's middle observation. The median depends on the number of observations. The value of the median is different if the number of observations is odd and different if the number of observations is even. This exercise class 10 ex 14.3 feature a variety of questions that cover the complete topic of determining the median in grouped data.
Exercise 14.3 Class 10 Maths also gives us information about what is cumulative frequency column, median class and also we will know about the relation between mean, median and mode. 10th class Maths exercise 14.3 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Let the assumed mean be a = 130 and h = 20
Class  Number of consumers  Cumulative Frequency  Classmark




6585  4  4  70  60  3  12 
85105  5  9  90  40  2  10 
105125  13  22  110  20  1  13 
125145  20  42  130  0  0  0 
145165  14  56  150  20  1  14 
165185  8  64  170  40  2  16 
185205  4  68  190  60  3  12 
= 68 
= 7 
MEDIAN:
Median class = 125145; Cumulative Frequency = 42; Lower limit, l = 125;
c.f. = 22; f = 20; h = 20
Thus, the median of the data is 137
MODE:
The class having maximum frequency is the modal class.
The maximum frequency is 20 and hence the modal class = 125145
Lower limit (l) of modal class = 125, class size (h) = 20
Frequency ( ) of the modal class = 20; frequency ( ) of class preceding the modal class = 13, frequency ( ) of class succeeding the modal class = 14.
Thus, Mode of the data is 135.76
MEAN:
Mean,
Thus, the Mean of the data is 137.05
Q2 If the median of the distribution given below is 28.5, find the values of x and y.
Class  Number of consumers  Cumulative Frequency 
010  5  5 
1020  x  5+x 
2030  20  25+x 
3040  15  40+x 
4050  y  40+x+y 
5060  5  45+x+y 
= 60 
Now,
Given median = 28.5 which lies in the class 2030
Therefore, Median class = 2030
Frequency corresponding to median class, f = 20
Cumulative frequency of the class preceding the median class, c.f. = 5 + x
Lower limit, l = 20; Class height, h = 10
Also,
Therefore, the required values are: x=8 and y=7
Class  Frequency
 Cumulative Frequency 
1520  2  2 
2025  4  6 
2530  18  24 
3035  21  45 
3540  33  78 
4045  11  89 
4550  3  92 
5055  6  98 
5560  2  100 
Therefore, Median class = 3545
Frequency corresponding to median class, f = 21
Cumulative frequency of the class preceding the median class, c.f. = 24
Lower limit, l = 35; Class height, h = 10
Thus, the median age is 35.75 years.
Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes. The classes then change to
117.5  126.5, 126.5  135.5, . . ., 171.5  180.5.)
The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes.
Class  Frequency
 Cumulative Frequency 
117.5126.5  3  3 
126.5135.5  5  8 
135.5144.5  9  17 
144.5153.5  12  29 
153.5162.5  5  34 
162.5171.5  4  38 
171.5180.5  2  40 
Therefore, Median class = 144.5153.5
Lower limit, l = 144.5; Class height, h = 9
Frequency corresponding to median class, f = 12
Cumulative frequency of the class preceding the median class, c.f. = 17
Thus, the median length of the leaves is 146.75 mm
Q5 The following table gives the distribution of the lifetime of 400 neon lamps :
Find the median lifetime of a lamp.
Class  Frequency
 Cumulative Frequency 
15002000  14  14 
20002500  56  70 
25003000  60  130 
30003500  86  216 
35004000  74  290 
40004500  62  352 
45005000  48  400 
Therefore, Median class = 30003500
Lower limit, l = 3000; Class height, h = 500
Frequency corresponding to median class, f = 86
Cumulative frequency of the class preceding the median class, c.f. = 130
Thus, the median lifetime of a lamp is 3406.97 hours
Thus, the median length of the leaves is 146.75 mm
Determine the median number of letters in the surnames. Find the mean number of
letters in the surnames? Also, find the modal size of the surnames.
Class  Number of surnames  Cumulative Frequency  Classmark


14  6  6  2.5  15 
47  30  36  5.5  165 
710  40  76  8.5  340 
1013  16  92  11.5  184 
1316  4  96  14.5  51 
1619  4  100  17.5  70 
= 100 
= 825 
MEDIAN:
Median class = 710; Lower limit, l = 7;
Cumulative frequency of preceding class, c.f. = 36; f = 40; h = 3
Thus, the median of the data is 8.05
MODE:
The class having maximum frequency is the modal class.
The maximum frequency is 40 and hence the modal class = 710
Lower limit (l) of modal class = 7, class size (h) = 3
Frequency ( ) of the modal class = 40; frequency ( ) of class preceding the modal class = 30, frequency ( ) of class succeeding the modal class = 16
Thus, Mode of the data is 7.88
MEAN:
Mean,
Thus, the Mean of the data is 8.25
Class  Number of students  Cumulative Frequency 
4045  2  2 
4550  3  5 
5055  8  13 
5560  6  19 
6065  6  25 
6570  3  28 
7075  2  30 
MEDIAN:
Median class = 5560; Lower limit, l = 55;
Cumulative frequency of preceding class, c.f. = 13; f = 6; h = 5
Thus, the median weight of the student is 56.67 kg
Class 10 Maths chapter 14 exercise 14 includes some of the basic questions in which we have to find the median of the grouped data. Along with this NCERT solutions for Class 10 Maths exercise 14.3 includes questions in which there is no class and we have to form the class of data ourselves. We also have to find all the central tendencies for some of the questions.
Exercise 14.3 Class 10 Maths covers all types of questions that can be formed in the median of grouped data and it has the question in which we have to find the frequency of the specific modal class. Moreover, there are few examples before NCERT solutions for Class 10 Maths exercise 14.3 that have questions that are based on the relation of mean, median and mode.
Also Read Statistics Class 10 Notes
Also, See:
Median gives the value of the observation which is at the center so it is dependent on either the observation is odd number or even number. Practice ex 14.3 class 10 to command these concepts.
The concept related to discusses in class 10 ex 14.3. Formula of median of odd observation is n/2th observation. Students can practice ex 14.3 class 10 to get deeper understanding of concepts.
The concepts related to median is discussed in class 10 maths ex 14.3. Formula of median of even observation is (n/2+ 1 )th observation. Also practice class 10 ex 14.3 which is discussed in this article to get deeper understanding of the concepts.
3 Median = Mode + 2 Mean is the relation between mean, medium and mode as mentioned in Class 10 maths chapter 14 exercise 14.3.
These concepts are discussed in 10th class maths exercise 14.3 answers. practice them to command the concepts. Cumulative Frequency Table is the cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
Hello
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Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
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