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
Kothanur, Bangalore
17 yrs of
Exp
18 students
552 hrs of classes completed
700
per hour
Student's Home
I am a Math and Hindi teacher with Aadya Academy, The World School Bangalore.I worked as a math and Hindi teacher with The Landmark school Rampura Bangalore for grades 7 to 10 for the last three years.I am an experienced, qualified teacher and tutor with over 17 years of experience in teaching Math and Hindi across different boards including CBSE, ICSE, and IGCSE for grade 7 to 12. I have 5 years of teaching experience with U. K based online company named FIRSTRING for GCSE, Edexcel and National curriculum of ENGLAND Syllabus . I am passionate about solving mathematical problems and helping students to understand easily. Over the years I have helped thousands of students overcome their fear of Math and Hindi Language.
Classes were good and no concerns. I took for 20th standard, one on one classes for subject mathematics.
Top Tutor
Vimanapura Krishna Nagar, Bangalore
6 yrs of
Exp
3 students
666 hrs of classes completed
600
per hour
Online Classes
Student's Home
In this competitive world education is the most important tool rather I say that it is sword by which one can win the competition.so I am in this field from last four years and teaching is my passion and even strength.My students are very happy with me in college as well as in tutions. Their results show it all. Students are always been encouraged to do studies one should not force them for the same.
Super Tutor
Choolissery, Thrissur
20 yrs of
Exp
12 students
373 hrs of classes completed
600
per hour
Online Classes
I was a teacher at a CBSE-affiliated school. I have six years of experience teaching on online platforms. I have been conducting Mathematics, Physics, and Chemistry classes for high school and higher secondary students for more than 20 years. I believe I can encourage and motivate students to achieve excellent academic results while inspiring them to develop good values and habits.
Sini ma'am is an excellent maths teacher. I joined her classes at exactly the right time when I needed clarity, and she explained every concept in a very simple and structured way. Her teaching style made even difficult topics easy to understand, and my confidence in maths improved a lot in a short period. She is very patient, supportive, and genuinely cares about her students’ understanding. I’m really grateful for the guidance and clarity she gave me.
Top Tutor
Nerul, Mumbai
6 yrs of
Exp
1 student
358 hrs of classes completed
400
per hour
Online Classes
Student's Home
Tutor's home
I have specifically guided Class 10 students for board exams, with a strong focus on NCERT syllabus, and topics like Real Numbers, Polynomials, Quadratic Equations, and Statistics. I provide regular tests, personalized feedback, and exam-oriented strategies to improve accuracy and speed. Many of my students have shown remarkable improvement and scored above 90% in their board exams.
Sir is very nice in explaining the concepts . He gives many question for me to practice and explains them in a simple and straightforward manner.
Top Tutor
Anna Nagar Western Extn, Chennai
7 yrs of
Exp
3 students
58 hrs of classes completed
500
per hour
Student's Home
Tutor's home
I am an experienced, qualified teacher and tutor with over 6 years of experience in teaching Maths across different boards including CBSE, ICSE, IGCSE and State Board. Passionate about solving mathematical problems. over the years I have helped hundred of students overcome their fear of Maths. I am a post graduates in mathematics and under graduates in education. We are available on both home tuition and online We have lot of success stories.
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
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
