Statistics

Important Questions

Here are some important questions for Class 10 Mathematics Chapter 13, Statistics, carefully selected to help students prepare effectively for the CBSE Class 10 Mathematics Examination in 2024-25. By practicing these diverse problems, students can improve their understanding of Statistics concepts and enhance their problem-solving abilities. These questions are designed to clarify doubts and contribute to better performance in the Statistics chapter.

Table of Contents

In Chapter 13 of Class 10 Mathematics,Statistics, we will focus on understanding and calculating the measures of central tendency—mean, median, and mode—for grouped data. These measures help us analyze and summarize large sets of data by providing insights into the typical values and trends within the data.

Statistics involves collecting, analyzing, and interpreting data to understand trends, patterns, and information in various fields. It helps in making informed decisions and drawing conclusions.

(b) The upper class boundary is the same as the lower class boundary of the next class.

(c) Both the lower and upper class boundaries are the same.

(d) The lower and upper class boundaries are contained within the class and do not intersect with either the upper boundary of the previous class or the lower boundary of the next class.

**Ans.**(d)

**Explanation:**

The lower and upper class boundaries are contained within the class and do not intersect with either the upper boundary of the previous class or the lower boundary of the next class.

**Ans.** (c) a \text{\={x}}

**Explanation:**

Mean of observations \space x_1 \space + \space x_2,\space …. \space x_n \space is \space \text{\={x}} \\
\space x_1 \space + \space x_2 \space + \space x_3 \space +, ….\space x_n = n \text{\={x}} \\[4.5 bp]
∴ \space x_1 + a + x_2 + a + x_3 + a + \space .......\space x_n + a \\[4.5 bp]
=\space x_1 + x_2 + x_3 +,\space …. \space x_n + na

∴ Mean of \space (x_1+x_2+x_3+\space ....\space +x_n)+ na

\\[4.5 bp] = \dfrac{n\text{\={x}} + na}{n}= \text{\={x}} + a

Marks | No. of students |
---|---|

5 | 6 |

10 | 4 |

15 | 6 |

20 | 12 |

25 | x |

30 | 4 |

**Explanation:**

Given Mean = 18

Marks | No. of students | Mid-value |
---|---|---|

(x_{i}) | (f_{i}) | f_{i }× x_{i} |

5 | 6 | 30 |

10 | 4 | 40 |

15 | 6 | 90 |

20 | 12 | 240 |

25 | x | 25x |

30 | 4 | 120 |

Total | 32 + x | 520 + 25x |

⇒ 576 + 18 x = 520 + 25x

⇒ 25x - 18x =576-520

⇒ 7x = 56

⇒ x = 8

Class Interval | Frequency |
---|---|

0-50 | 4 |

50-100 | 8 |

100-150 | 16 |

150-200 | 13 |

200-250 | 6 |

250-300 | 3 |

**Explanation:**

Class Interval | Frequency (f_{i} ) | Class Marks (x_{i}) | (f_{i} x_{i}) |
---|---|---|---|

0-50 | 4 | 25 | 100 |

50-100 | 8 | 75 | 600 |

100-150 | 16 | 125 | 2000 |

150-200 | 13 | 175 | 2275 |

200-250 | 6 | 225 | 1350 |

250-300 | 3 | 275 | 825 |

N = Σf_{i} = 50 | (f_{i} x_{i}) =7150 |

**Explanation:**

Thus,

Mean = Σf_ix_i/Σf_i = 7150/50

= 143

**Explanation:**

Daily Expenditure (in ₹ ) | No. of Households (f _{i}) | Mid-value ( x _{i}) | f_{i }× x_{i} |
---|---|---|---|

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 |

Σx_{i }=25 | Σx_{i }f_{i }= 5275 |

**Explanation:**

\therefore \space \space \space \text{Mean } (\bar{x}) = \dfrac{\Sigma f_i \space x_i}{\Sigma f_i} = \dfrac{5275}{25} = 211\\[2.5 bp]
Hence, Mean = 211

Chapter No. | Chapter Name |
---|---|

Chapter 1 | Real Numbers |

Chapter 2 | Polynomials |

Chapter 3 | Pair of Linear Equations in Two Variable |

Chapter 4 | Quadratic Equations |

Chapter 5 | Arithmetic Progressions |

Chapter 6 | Triangles |

Chapter 7 | Coordinate Geometry |

Chapter 8 | Introduction to Trigonometry |

Chapter 9 | Some Applications of Trigonometry |

Chapter 10 | Circles |

Chapter 11 | Areas Related to Circle |

Chapter 12 | Surface Areas and Volumes |

Chapter 13 | Statistics |

Chapter 14 | Probability |

To enhance your grasp of the Statistics chapter, consider exploring oswal.io. This website provides a variety of practice questions tailored to facilitate better learning. By engaging with these questions, you can reinforce your understanding of statistical concepts and improve your problem-solving abilities in this important math topic.

Ans: Data refers to information or observations collected for analysis. Raw data is the original, unprocessed form of data before any organization or manipulation.

Ans: Statistics is a branch of mathematics that involves collecting, organizing, analyzing, interpreting, and presenting data. It provides methods for understanding patterns, trends, and relationships in data.

Ans: The median is the middle value of a dataset when arranged in ascending or descending order. It divides the data into two equal halves.

Ans: Grouped data is data that is categorized into intervals or classes. It simplifies data representation when dealing with large datasets.

Ans: The midpoint of a class interval is calculated by adding the lower and upper limits of the interval and dividing by 2.

Chapter Wise Important Questions for CBSE Board Class 10 Maths |
---|

Real Numbers |

Polynomials |

Pair of Linear Equations in Two Variables |

Quadratic Equations |

Arithmetic Progressions |

Triangles |

Coordinate Geometry |

Introduction to Trigonometry |

Some Applications of Trigonometry |

Circles |

Areas Related to Circles |

Surface Areas and Volumes |

Statistics |

Probability |

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