Class 10 Math Chapter 13
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 2023-24. 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.

Introduction

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.

What is the purpose of statistics in mathematics?

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.

Class 10 Statistics Important Questions and Answers

Q1.  In an inclusive series :

Options

(a) The lower class boundary is the same as the upper class boundary of the previous class.
(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.

Q2. Find the Class marks of class 10 – 25 and 35 – 55.

Options

(a)1.75 and 45
(b)17.5 and 4.5
(c)1.75 and 4.5
(d)17.5 and 45

Ans. (b)17.5 and 4.5

Explanation:
Explanation: We derive the class mark x_i by the following formula :

x_i=\(\frac{1}{2}\) (lower limit + upper limit)
Thus, x_i=\(\frac{1}{2}\)(10 + 25)
=\(\frac{1}{2}\)(35)=17.5
And x_ii = \(\frac{1}{2}\) (lower limit + upper limit)
Thus, x_ii =\(\frac{1}{2}\)(35 + 55)
=\(\frac{1}{2}\)(90) = 45

Q3. The table below shows the distribution of marks obtained by students in an examination. Calculate the value of x if the mean mark is 18.

Ans.  x = 8

Explanation:
Given Mean = 18

Mean = \(\frac{\Sigma f_ix_i}{\Sigma f_i}\)
18 = 520 + 25 x/32+ x
 18(32+x)  = 520 +25x       
576-520 = 25x-18x              
 X = 8

Q4. Find the mean of the following frequency distribution:

Ans. Mean = 143

Explanation:‍

Explanation:
Mean =  Σf_ix_i/Σf_i = 7150/50                 
= 143

Q5. In a class of 30 students, the heights (in cm) of the students are recorded as follows: 140, 142, 145, 150, 148, 152, 156, 145, 146, 144, 149, 151, 153, 148, 142, 147, 149, 155, 146, 144, 147, 150, 153, 147, 145, 149, 151, 153, 152, 148. Calculate the mean height of the students.

Ans. 149.2

Explanation:
Sum up all the heights: Sum = 140 + 142 + 145 + 150 + 148 + 152 + 156 + 145 + 146 + 144 + 149 + 151 + 153 + 148 + 142 + 147 + 149 + 155 + 146 + 144 + 147 + 150 + 153 + 147 + 145 + 149 + 151 + 153 + 152 + 148
Sum = 4476
Calculate the mean: 
Mean = Sum / Total number of students 
Mean = 4476 / 30 
Mean = 149.2 cm

CBSE Class 10 Maths Chapter   wise Important Questions

Conclusion

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.

Frequently Asked Questions

Q1: Define 'data' and 'raw data.

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

Q2: What is statistics?

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.

Q3: Define median.

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.

Q4: Explain the concept of 'grouped data’.

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

Q5: How is the 'midpoint' of a class interval calculated?

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