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Home / Board / ICSE / important Questions / Class 10 / Maths / Statistics

Class 10 Maths Chapter 19
Statistics
Important Questions

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In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, Chapter 19 delves into the fascinating world of “Statistics.” Statistics is the mathematical discipline that deals with the collection, analysis, interpretation, and presentation of data. This chapter equips students with the tools and knowledge to work with data effectively. Here’s an introduction to statistics class 10 ICSE important questions.

Introduction

In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, the chapter on “Statistics” is an essential topic that explores the fascinating field of data collection, analysis, interpretation, and presentation. Statistics is a branch of mathematics that helps us make sense of the vast amounts of data we encounter in our lives. Here’s an introduction to the topic of statistics in Class 10 ICSE mathematics:
Key Concepts and Objectives:
Data: Data refers to the raw facts, numbers, or information collected from various sources. It can be qualitative or quantitative.
Data Sets: Data sets are collections of data points or observations. They form the basis for statistical analysis.
‍Data Collection: Statistics involves the methods and techniques for collecting data, whether through surveys, experiments, observations, or research.
Data Organization: To make data more manageable, it is organized using techniques like frequency distribution and histograms.
Measures of Central Tendency: These measures, including the mean (average), median (middle value), and mode (most frequent value), help describe the center or typical value of a data set.

What is Statistics?

Statistics is like a magical toolkit that helps you tame and understand data. It’s the art and science of working with information, turning it into knowledge, and using that knowledge to make smart decisions. Think of it as your secret weapon for unraveling the mysteries hidden within numbers. Statistics can be likened to a versatile toolbox that empowers you to decode and make sense of data. It’s both an art and a science, where you transform raw information into valuable insights, equipping you to make informed and intelligent choices.
statistics class 10 icse important questions

Class 10 Statistics Important Questions and Answers

Q1. Find the mean of the following distribution:
Heights (in cms)No. of Sticks
1510
1816
2010
228
257
3010
Options
(a) 21·18
(b) 21·36
(c) 21·54
(d) none

Ans. (a) 21·18
Explanation:
Σf = 10 + 15 + 10 + 8 + 7 + 10 = 60   
Σfx = 150 + 270 + 200 + 176 + 175 + 300  
= 1271
∴  Mean  = \frac{\Sigma fx}{\Sigma f} = \frac{1271}{60} =21.18.

Q2. Find the curved surface area of the solid cylinder of diameter 21 cm and height 15 cm.
Options
(a) 345 cm2
(b) 315 cm2
(c) 630 cm2
(d) 990 cm2

Ans. (d) 990 cm^2\\ Explanation:
Radius (r) = \frac{1}{2} × diameter = \frac{21}{2} cm
Height (k) = 15 cm
∴ curnel surface area =2πrh
=2× \frac{21}{7} × \frac{21}{2}×15 \\ = 990  cm^2.

Q3.Using step-deviation method, find the mean of following frequency distribution :
X1030507090110
Y135187240273124151

Explanation:
Let the assumed mean A = 70.

xfd= x – Aft
10135– 60– 3– 405
30187– 40– 2– 374
50240– 20– 1– 240
A = 70273000
90124201124
110151402302

Explanation:
Mean =A + \frac{\Sigma ft}{\Sigma f} × i \\ =70+ \begin{pmatrix}   \frac{-593}{1110}\end{pmatrix} ×20 = 59.32 ans.

Q4. The mean of n observations
x_1, x_2,.....  x_n \space is \space \bar{X}.(a – b) is added to each of the observation, show that the mean of the new set of observations is \bar{X} (a−b).

Explanation:
we have
\bar{X} = \frac{x_1+x_2+..+x_n}{n} .....(i)\\ \text{Let} \\ \bar{X} = \text{be the mean of}  x_1 + (a,b) x_2+(a-b),..., x_n+(a-b).\\ \text{Then}\\ \bar{X} = \frac{[x_1+(a-b)]+[x_2(a-b)]+..+[x_n(a-b)]}{n} \\ = \frac{x_1+x_2+..+x_n+n(a-b)}{n} \\ = \frac{x_1+x_2+..+x_n}{n} = \frac{n(a-b)}{n} \\ = \bar{X} +(a−b). [Using (i)]

Q5. The mean monthly salary of 10 members of a group is ₹ 1,445, one more member whose monthly salary is ₹ 1,500 has joined the group. Find the mean monthly salary of 11 members of the group.
(a) Slope of BC,
(b) Equation of a line perpendicular of BC and passing through A.

Explanation:
Here, n=10, \bar{X} =1445. So, \bar{X} = \frac{1}{n}(∑ x_1​ ) \\ ⇒ n \bar{X} = ∑ x_1 \\ ⇒    10×1445 = ∑ x_1 \\ ⇒    ∑ x_1 = 14450. So, total monthly salary of 10 persons is ₹ 14,450.Monthly salary of one more person who joined the group is ₹ 1,500.
∴  Total monthly salary of 11 persons = ₹14,450 +₹1,500 = ₹15,950
So, average monthly salary of 11 persons= \frac{Total\space monthly\space salery}{11} = \frac{15,950}{11} = ₹ 1,450.

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ICSE Class 10 Maths Chapter wise Important Questions

Chapter No.Chapter Name
Chapter 1Goods and Service Tax (GST)
Chapter 2Banking
Chapter 3Shares and Dividends
Chapter 4Linear inequations
Chapter 5Quadratic Equations in one variable
Chapter 6Ratio and proportion
Chapter 7Factorization
Chapter 8Matrices
Chapter 9Arithmetic Progression
Chapter 10Geometric Progression
Chapter 11Coordinate Geometry
Chapter 12Reflection
Chapter 13Similarity
Chapter 14Loci
Chapter 15Circles
Chapter 16Constructions
Chapter 17Mensuration
Chapter 18Trigonometry
Chapter 19Statistics
Chapter 20Probability

Conclusion

In conclusion, the study of statistics in ICSE Class 10 mathematics is a fundamental and empowering journey into the world of data. It equips students with the skills to collect, organize, analyze, interpret, and present information effectively. Statistics is not just about numbers; it’s about making informed decisions, solving real-world problems, and understanding the patterns that shape our lives. With a solid foundation in statistics, students are better prepared to navigate the data-rich landscape of the modern world, from academic pursuits to making informed choices in various aspects of life. It’s a valuable tool that unlocks a wealth of knowledge and empowers individuals to be data-savvy and informed citizens. For those looking to enhance their grasp of the chapter’s content and gain extra practice, oswal.io provides statistics class 10 ICSE important questions that can help foster a more thorough comprehension of the concepts.

Frequently Asked Questions

Ans: Statistics is used to collect, analyze, and interpret data, enabling us to make informed decisions and draw meaningful conclusions from information.
Ans: Data is raw information or facts collected for analysis. It’s crucial in statistics because it forms the basis for drawing conclusions and making predictions.
Ans: Data can be organized using methods like frequency distribution, grouping data into classes, and creating histograms or bar graphs.
Ans: Measures of central tendency, including the mean, median, and mode, help describe the center or typical value of a data set.
Ans: The range is the difference between the maximum and minimum values in a data set. It indicates the spread or variability of the data.
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CBSE Important Questions Class 10

ICSE Important Questions Class 10

CBSE Important Questions Class 10

ICSE Important Questions Class 10

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