Aakash Repeater Courses
Take Aakash iACST and get instant scholarship on coaching programs.
Statistics enables us to understand real-life data through interpretation of collected information. This field in mathematics handles the process of gathering numerical data followed by visual or analytical interpretation to reveal statistical patterns. The exercise works with grouped data together with frequency distribution patterns to analyze large statistical information. The procedure of grouping data followed by counting the number of occurrences in each category enables us to find significant patterns.
This Story also Contains
The NCERT Solutions for Exercise 13.1 represent unprocessed data through grouped frequency tables. The frequency tables demonstrate to students which values occur in which intervals. The exercise challenges students to convert raw data into structured forms which lays a foundation for computing mean, median and mode values in future assignments. The exercise functions as an essential tool for knowledge described in NCERT Books which leads to complete understanding of problems and their practical applications.
Which method did you use for finding the mean, and why?
Number of plants | Number of houses | Classmark | |
0-2 | 1 | 1 | 1 |
2-4 | 2 | 3 | 6 |
4-6 | 1 | 5 | 5 |
6-8 | 5 | 7 | 35 |
8-10 | 6 | 9 | 54 |
10-12 | 2 | 11 | 22 |
12-14 | 3 | 13 | 39 |
=20 | =162 |
Mean,
We used the direct method in this as the values of
Q2 Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.
Let the assumed mean be a = 550
Daily Wages | Number of workers | Classmark | | |
500-520 | 12 | 510 | -40 | -480 |
520-540 | 14 | 530 | -20 | -280 |
540-560 | 8 | 550 | 0 | 0 |
560-580 | 6 | 570 | 20 | 120 |
580-600 | 10 | 590 | 40 | 400 |
= 50 | = -240 |
Mean,
Therefore, the mean daily wages of the workers of the factory is Rs. 545.20
Daily pocket allowance | Number of children | Classmark | |
11-13 | 7 | 12 | 84 |
13-15 | 6 | 14 | 84 |
15-17 | 9 | 16 | 144 |
17-19 | 13 | 18 | 234 |
19-21 | f | 20 | 20f |
21-23 | 5 | 22 | 110 |
23-25 | 4 | 24 | 96 |
=44+f | =752+20f |
Mean,
Therefore the missing f = 20
Let the assumed mean be a = 75.5
No. of heartbeats per minute | Number of women | Classmark | | |
65-68 | 2 | 66.5 | -9 | -18 |
68-71 | 4 | 69.5 | -6 | -24 |
71-74 | 3 | 72.5 | -3 | -9 |
74-77 | 8 | 75.5 | 0 | 0 |
77-80 | 7 | 78.5 | 3 | 21 |
80-83 | 4 | 81.5 | 6 | 24 |
83-86 | 2 | 84.5 | 9 | 18 |
=30 | =12 |
Mean,
Therefore, the mean heartbeats per minute of these women are 75.9
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Let the assumed mean be a = 57
Number of mangoes | Number of boxes | Classmark | | |
50-52 | 15 | 51 | -6 | -90 |
53-55 | 110 | 54 | -3 | -330 |
56-58 | 135 | 57 | 0 | 0 |
59-61 | 115 | 60 | 3 | 345 |
62-64 | 25 | 63 | 6 | 150 |
=400 | =75 |
Mean,
Therefore, the mean number of mangoes kept in a packing box is approx 57.19
Q6 The table below shows the daily expenditure on the food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.
Daily expenditure in rupees | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |
Number of households | 4 | 5 | 12 | 2 | 2 |
Let the assumed mean be a = 225 and h = 50
Daily Expenditure | Number of households | Classmark | | | |
100-150 | 4 | 125 | -100 | -2 | -8 |
150-200 | 5 | 175 | -50 | -1 | -5 |
200-250 | 12 | 225 | 0 | 0 | 0 |
250-300 | 2 | 275 | 50 | 1 | 2 |
300-350 | 2 | 325 | 100 | 2 | 4 |
=25 | = -7 |
Mean,
Therefore, the mean daily expenditure on food is Rs. 211
Find the mean concentration of
Class Interval | Frequency | Classmark | |
0.00-0.04 | 4 | 0.02 | 0.08 |
0.04-0.08 | 9 | 0.06 | 0.54 |
0.08-0.12 | 9 | 0.10 | 0.90 |
0.12-0.16 | 2 | 0.14 | 0.28 |
0.16-0.20 | 4 | 0.18 | 0.72 |
0.20-0.24 | 2 | 0.22 | 0.44 |
=30 | =2.96 |
Mean,
Therefore, the mean concentration of
Number of days | Number of Students | Classmark | |
0-6 | 11 | 3 | 33 |
6-10 | 10 | 8 | 80 |
10-14 | 7 | 12 | 84 |
14-20 | 4 | 17 | 68 |
20-28 | 4 | 24 | 96 |
28-38 | 3 | 33 | 99 |
38-40 | 1 | 39 | 39 |
=40 | =499 |
Mean,
Therefore, the mean number of days a student was absent is 12.48 days.
Let the assumed mean be a = 75 and h = 10
Literacy rates | Number of cities | Classmark | | | |
45-55 | 3 | 50 | -20 | -2 | -6 |
55-65 | 10 | 60 | -10 | -1 | -10 |
65-75 | 11 | 70 | 0 | 0 | 0 |
75-85 | 8 | 80 | 10 | 1 | 8 |
85-95 | 3 | 90 | 20 | 2 | 6 |
= 35 | = -2 |
Mean,
Therefore, the mean mean literacy rate is 69.43%
Also Read-
Take Aakash iACST and get instant scholarship on coaching programs.
1. Grouped Frequency Distribution: A person must learn to convert extensive raw data into classification intervals combined with frequency counts that produce better reading metrics.
2. Mid-point Method: The average calculation for grouped data requires using the midpoints from class intervals to estimate the central value.
3. Mean of Grouped Data: The formula Mean = (∑fx) / ∑f applies to calculate grouped data average while recognizing f as the frequency and x as the class mark (midpoint).
4. Data Interpretation: The skill involves understanding real-world data followed by tabular structure implementation for better analysis purposes.
5. Practical Understanding of Statistics: Data handling abilities prove essential in practical conditions like budgeting surveys and planning and budget processes.
Check Out-
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Frequently Asked Questions (FAQs)
To find what is the basics of statistic. Definition of mean and its formula. To learn about different methods of finding mean like Assumed mean method, step deviation method etc. Go through the ex 14.1 class 10 to command these concepts.
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. Practice class 10 maths ex 14.1 to command these concepts.
The class midpoint (or class mark) is a specific point in the centre of the bins (categories) in a frequency distribution table. Go through exercise 14.1 class 10 maths to get deeper understanding of concepts.
This class 10 ex 14.1 discusses the concept of mean in detail. to find mean of data use formula discussed in this exercise. mean = sum of total data / number of data
The centre of a bar in a histogram is known as class mark.
The mean of the data will also increase by 5.
On Question asked by student community
Hello
You asked about Class 10 sample paper board exam and most important questions. Practicing sample papers and previous year questions is one of the best ways to prepare for the board exam because it gives a clear idea of the exam pattern and types of questions asked. Schools and teachers usually recommend students to solve at least the last five years question papers along with model papers released by the board.
For Class 10 board exams, the most important areas are Mathematics, Science, Social Science, English, and Hindi or regional language. In Mathematics, questions from Algebra, Linear Equations, Geometry, Trigonometry, Statistics, and Probability are repeatedly seen. For Science, the key chapters are Chemical Reactions, Acids Bases and Salts, Metals and Non metals, Life Processes, Heredity, Light and Electricity. In Social Science, priority should be given to Nationalism, Resources and Development, Agriculture, Power Sharing, Democratic Politics, and Economics related topics. In English, focus on unseen passages, grammar exercises, and important writing tasks like letter writing and essays.
Follow these steps to access the SQPs and marking schemes:
Step 1: Visit https://cbseacademic.nic.in/
Step 2: Click on the link titled “CBSE Sample Papers 2026”
Step 3: A PDF will open with links to Class 10 and 12 sample papers
Step 4: Select your class (Class 10 or Class 12)
Step 5: Choose your subject
Step 6: Download both the sample paper and its marking scheme
Hello,
Yes, you can give the CBSE board exam in 2027.
If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.
Hope it helps !
Here are some strategies so u can do best in your board exams and get god score
1. Make a good and smart schedule
2. If u r from cbse board go through ncert books by heart
3. Solve pyqs of each subject
4. Do revision on daily basis
5. Practice on presentation and writing the answer .
6. Do your best and give exam with the best way possible all the best blud .
Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.
Hello Aspirant,
Here's how you can find it:
School ID Card: Your registration number is often printed on your school ID card.
Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.
School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.
Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.
Your school is the best place to get this information.
Take Aakash iACST and get instant scholarship on coaching programs.
This ebook serves as a valuable study guide for NEET 2025 exam.
This e-book offers NEET PYQ and serves as an indispensable NEET study material.
As per latest syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE