Find the best tutors and institutes for Class 10 Tuition
Q7:
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Solution :
Given: A frequency distribution of the weights of 30 students.
| Weight (kg) | Number of students (f) |
|---|---|
| 40 - 45 | 2 |
| 45 - 50 | 3 |
| 50 - 55 | 8 |
| 55 - 60 | 6 |
| 60 - 65 | 6 |
| 65 - 70 | 3 |
| 70 - 75 | 2 |
To Find: The median weight of the students.
Step 1: Constructing the Cumulative Frequency Table
To find the median, we must first calculate the cumulative frequency ($cf$) for each class interval.
| Weight (kg) | Frequency ($f$) | Cumulative Frequency ($cf$) |
|---|---|---|
| 40 - 45 | 2 | 2 |
| 45 - 50 | 3 | 2 + 3 = 5 |
| 50 - 55 | 8 | 5 + 8 = 13 |
| 55 - 60 | 6 | 13 + 6 = 19 |
| 60 - 65 | 6 | 19 + 6 = 25 |
| 65 - 70 | 3 | 25 + 3 = 28 |
| 70 - 75 | 2 | 28 + 2 = 30 |
| Total | $n = 30$ | - |
Step 2: Identifying the Median Class
The total number of observations is $n = 30$.
We calculate $\frac{n}{2} = \frac{30}{2} = 15$.
[The median class is the class interval whose cumulative frequency is greater than or nearest to $\frac{n}{2}$.]
Looking at the table, the cumulative frequency just greater than 15 is 19, which corresponds to the class interval 55 - 60.
Step 3: Applying the Median Formula
The formula for the median is:
$Median = l + \left( \frac{\frac{n}{2} - cf}{f} \right) \times h$
Where:
$l$ (lower limit of median class) = $55$
$n$ (total number of observations) = $30$
$cf$ (cumulative frequency of the class preceding the median class) = $13$
$f$ (frequency of the median class) = $6$
$h$ (class size) = $60 - 55 = 5$
Step 4: Calculating the Result
$Median = 55 + \left( \frac{15 - 13}{6} \right) \times 5$
$Median = 55 + \left( \frac{2}{6} \right) \times 5$
$Median = 55 + \left( \frac{1}{3} \right) \times 5$
$Median = 55 + \frac{5}{3}$
$Median = 55 + 1.666...$
$Median \approx 56.67$
Final Answer: The median weight of the students is 56.67 kg.
More Questions from Class 10 Mathematics Statistics EXERCISE 13.3
- Q1: The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
- Q2: If the median of the distribution given below is 28.5, find the values of $x$ and $y$.
- Q3: A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
- Q4: The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table : 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.)
- Q5: The following table gives the distribution of the life time of 400 neon lamps : Find the median life time of a lamp.
- Q6: 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: 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.
CBSE Solutions for Class 10 Mathematics Statistics
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Statistics
Top Tutor
Sector 49 South City II, Gurgaon
16 yrs of
Exp
500
per hour
Online Classes
Student's Home
I am an engineer and i have been teaching for the past 16 years. I put stress on the clarification of the basic concepts of the subject. I teach maths and science.
Top Tutor
Thane West, Thane
16 yrs of
Exp
17 students
3717 hrs of classes completed
350
per hour
Online Classes
This is Debabrato Chatterjee, an Maths and Science tutor with more than fifteen years of experience. I have been and am teaching students of IB, IGCSE, CBSE, ICSE, and Maharastra State Boards. My teaching style is to learning from concepts and their application. Solving many papers and completing homework helps grasp the concepts. I teach students from grade VI to XII. Please let me know when you would like to schedule a demo.
Top Tutor
Gharoli Gharoli, Delhi
16 yrs of
Exp
1 student
23 hrs of classes completed
2000
per hour
Online Classes
I bring with me 17 years of diverse experience in the pharmaceutical industry along with academic expertise, combining strong practical knowledge with a passion for teaching. I am dedicated to simplifying complex concepts and delivering them in an engaging manner, ensuring that students not only gain subject knowledge but also develop the skills, confidence, and potential required to achieve academic excellence and become industry-ready professionals.
I highly recommend this teacher to anyone looking for a clear and effective learning experience. The teaching style is simple, engaging, and easy to follow, which makes even difficult topics understandable. Every chapter is explained in depth, with attention to important concepts and details, ensuring that students build a strong foundation. The teacher is patient, knowledgeable, and dedicated to helping students succeed. Lessons are well-structured, and examples are used effectively to make learning more practical and enjoyable. This approach boosts confidence, improves understanding, and encourages active participation. Overall, an excellent teacher who makes learning both meaningful and enjoyable.
Top Tutor
Sector 150, Noida
5 yrs of
Exp
800
per hour
Student's Home
Tutor's home
Having 2 years experience in teaching class 6th to 10th across different boards.
Top Tutor
Sector-63 Mohali, Chandigarh
5 yrs of
Exp
1 student
11 hrs of classes completed
500
per hour
Online Classes
Tutor's home
I have been tutoring students from past 6 years and as a professional School teacher from past 4 years . I know what is the competition and how to make student competent to face that with effective learning material and concept clarity .
Excellent experience. Service was wonderful. There was ambience habitat. All the things was understand easily.
Find more Tutor for Statistics in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
