Class 10 Maths Chapter 13 Statistics Overview
NCERT Solutions for Class 10 Maths Chapter 13 – Statistics are available here in an easy-to-access format. The solutions help students develop a complete understanding of statistical concepts which enables them to solve all exercise problems with confidence. The solution presents a detailed explanation which enables students to understand the proper calculation procedure.
The solved questions are prepared according to the latest NCERT syllabus guidelines. Regular practice of these solutions enables students to achieve a better understanding of mean, median, mode, cumulative frequency, and graphical representation. The students achieve better results in their Class 10 board exams because they participate in this organized study approach.
Class 10 Maths Chapter 13 – Statistics
Chapter 13 Statistics stands as the most crucial section of Class 10 Mathematics. The board examination contains multiple questions from this unit because it holds high weight for students. The exam pattern determines which type of questions students will answer, with marks distributed between short and long answer questions. Students need to practice this chapter because it holds high importance for their studies.
Topics Covered in Chapter 13 – Statistics
- Mean of Grouped Data
- Mode of Grouped Data
- Median of Grouped Data
- Graphical Representation of Cumulative Frequency Distribution
These topics help students understand how to collect, organize, analyze, and represent data properly.
Why Statistics Is Important
Statistics is a very practical branch of mathematics. Today, the world is data-driven. Every field such as business, sports, education, and research uses data to make decisions. Statistics helps in presenting data in a meaningful and easy-to-understand way.
In this chapter, students learn important methods such as:
- Direct method and step-deviation method for finding mean
- Finding median and mode of grouped data
- Relationship between mean, median, and mode
- Converting frequency distribution
- Drawing cumulative frequency curves (ogive)
These methods are useful not only in exams but also in real-life situations where data needs to be analyzed.
How ToppersSky Helps in Chapter 13 Preparation
ToppersSky offers NCERT Solutions for Class 10 Maths Chapter 13 in a structured format which includes detailed explanations through step-by-step methods. The methods used in solving questions are simple and easy to understand which helps students learn basic statistics concepts.
With Animation learning videos, practice sets, notes, and revision support available on the topperssky app, students can strengthen their concepts and prepare effectively for exams.
Key Features of ToppersSky NCERT Solutions for Chapter 13
- Complete solutions to all exercise questions
- Clear explanation of calculation methods
- Helpful reference material for quick revision
- Structured approach for better understanding
- Based on the latest NCERT syllabus guidelines
- Designed to improve accuracy and problem-solving skills
Students can achieve good results in Statistics while developing their analytical abilities through persistent practice and complete comprehension of all available methods.
Q.1 A survey recorded the number of plants in 20 houses. Find the mean number of plants per house.
Solution:
| Class Interval | Frequency (fi) | Class Mark (xi) | fi × xi |
|---|---|---|---|
| 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 |
| Total | 20 | 162 |
Mean = Σfi xi / Σfi
= 162 / 20
= 8.1 plants
Method used: Direct Method (because numbers are small).
Q.2 Find the mean daily wages of 50 workers.
| Class | fi | xi | fi xi |
|---|---|---|---|
| 500–520 | 12 | 510 | 6120 |
| 520–540 | 14 | 530 | 7420 |
| 540–560 | 8 | 550 | 4400 |
| 560–580 | 6 | 570 | 3420 |
| 580–600 | 10 | 590 | 5900 |
| Total | 50 | 27260 |
Mean = 27260 / 50
= ₹545.2
Q.3 Mean pocket allowance = ₹18. Find missing frequency (f).
After applying the assumed mean method and solving:
Missing frequency f = 20
Q.4 Find the mean heartbeats per minute.
| Class | fi | xi | fi xi |
|---|---|---|---|
| 65–68 | 2 | 66.5 | 133 |
| 68–71 | 4 | 69.5 | 278 |
| 71–74 | 3 | 72.5 | 217.5 |
| 74–77 | 8 | 75.5 | 604 |
| 77–80 | 7 | 78.5 | 549.5 |
| 80–83 | 4 | 81.5 | 326 |
| 83–86 | 2 | 84.5 | 169 |
| Total | 30 | 2277 |
Mean = 2277 / 30
= 75.9 beats per minute
Q.5 Mean number of mangoes per box.
Using Step-Deviation Method:
Mean ≈ 57.19 mangoes
Method chosen because class intervals are equal and numbers are large.
Q.6 Mean daily food expenditure.
| Class | fi | xi | fi xi |
|---|---|---|---|
| 100–150 | 4 | 125 | 500 |
| 150–200 | 5 | 175 | 875 |
| 200–250 | 12 | 225 | 2700 |
| 250–300 | 2 | 275 | 550 |
| 300–350 | 2 | 325 | 650 |
| Total | 25 | 5275 |
Mean = 5275 / 25
= ₹211
Q.7 Find mean concentration of SO₂.
| Class | fi | xi | fi xi |
|---|---|---|---|
| 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 |
| Total | 30 | 2.96 |
Mean = 2.96 / 30
= 0.0987 ppm
Q.8 Mean absentee days.
| Class | fi | xi | fi xi |
|---|---|---|---|
| 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 |
| Total | 40 | 499 |
Mean = 499 / 40
= 12.48 days
Q.9 Mean literacy rate.
| Class | fi | xi | fi xi |
|---|---|---|---|
| 45–55 | 3 | 50 | 150 |
| 55–65 | 10 | 60 | 600 |
| 65–75 | 11 | 70 | 770 |
| 75–85 | 8 | 80 | 640 |
| 85–95 | 3 | 90 | 270 |
| Total | 35 | 2430 |
Mean = 2430 / 35
= 69.43%
Q.10 The following table shows the marks obtained by 60 students in a test. Find the mean marks using the step-deviation method.
| Marks | Number of Students |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 12 |
| 30–40 | 15 |
| 40–50 | 10 |
| 50–60 | 10 |
First, find class marks (xi):
0–10 → 5
10–20 → 15
20–30 → 25
30–40 → 35
40–50 → 45
50–60 → 55
Take assumed mean (A) = 35
Class width (h) = 10
Now calculate:
| xi | fi | ui = (xi − A)/h | fi ui |
|---|---|---|---|
| 5 | 5 | -3 | -15 |
| 15 | 8 | -2 | -16 |
| 25 | 12 | -1 | -12 |
| 35 | 15 | 0 | 0 |
| 45 | 10 | 1 | 10 |
| 55 | 10 | 2 | 20 |
Total frequency (Σfi) = 60
Σfiui = -13
Now,
Mean = A + (Σfiui / Σfi) × h
35 + (-13/60) × 10
=35 − 2.17
= 32.83
FAQs
1. Why is Statistics an important chapter in Class 10 Maths?
The board examination gives the Statistics chapter important value because it requires students to use mathematical skills in practical situations. The system teaches students how to collect and systematize information so they can create useful data presentations. The chapter contains numerical questions which require students to learn specific methods so they can achieve high scores through dedicated study.
2. What are the main formulas to remember in Chapter 14?
The chapter establishes essential formulas which students must memorize to calculate the mean through direct and step-deviation methods and median of grouped data and mode of grouped data and mean- median- mode relationship. The formulas function as fundamental requirements needed to complete most numerical assignments within the chapter. Understanding how and when to apply each formula is more important than just memorizing them.
3. How can I improve my calculation speed in Statistics?
Students can improve their calculation speed by practicing numerical problems regularly and revising formulas daily. The process of solving sample papers and previous year questions creates the path toward building confidence. Step-by-step solutions together with common calculation errors should receive student attention because they enhance both accuracy and speed during testing.
4. What type of questions are usually asked from Statistics in exams?
The exam questions require students to calculate mean, median, and mode from grouped data and create cumulative frequency tables and produce graphical representations which include ogives. Long answer numerical questions are common in this chapter, so students should practice presenting solutions clearly and systematically.
5. What is the best way to revise Chapter 14 before exams?
The best way to improve this chapter requires the author to summarize key formulas from all processes and demonstrate their application through two sample exercises and present a new method for creating graphical displays. Students should check their earlier errors and ask questions to their teachers before the test. The practice of short study sessions throughout the day enables students to remember information for extended periods.
