Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sec A
1. Given the data set: 2, 5, 3, 8, 6, find the mode.
2. What is a histogram, and how does it differ from a bar graph?
Sec B
1. Calculate the median of the following data set: 4, 8, 15, 16, 23.
2. What is the range of the following data set: 10, 15, 8, 12, 20?
Sec C
A random survey of the number of children of various age groups playing in a park was found as follows.
| Age (in years) | Number of children |
|---|---|
| 1 - 2 | 5 |
| 2 - 3 | 3 |
| 3 - 5 | 6 |
| 5 - 7 | 12 |
| 7 - 10 | 9 |
| 10 - 15 | 10 |
| 15 - 17 | 4 |
Draw a histogram to represent the data above.
Sec D
Draw a histogram for the daily earnings of 30 drug stores in the following table.
| Daily earnings (in ₹) | 450 - 500 | 500 - 550 | 550 - 600 | 600 - 650 |
|---|---|---|---|---|
| Number of Stores | 16 | 10 | 7 | 3 |
Value-Based Questions
Problem 1
Question:The students in a class decide to collect data on the number of hours they study every day and represent it in the form of a frequency distribution table. After collecting the data, they calculate the mean number of study hours. How can this statistical exercise help students understand the importance of time management and self-discipline in academics?
Problem 2
Question:A school conducted a survey to find out the favorite extracurricular activities of students. The data collected was represented in the form of a bar graph and analyzed using statistical measures like mode and median. Explain how this activity can promote inclusivity and help the school plan events that cater to the interests of all students.
Problem 3
Question:In a village, health workers collect data on the number of people who visit the health clinic each day over a month. Using statistical tools like mean, median, and mode, they analyze the data to find the busiest days. How does this statistical analysis support public health management and reflect the value of ensuring well-being in a community?
HOTS
Q1
In a class of 40 students, the marks obtained by students in a math test are grouped into the following intervals: 0-10, 10-20, 20-30, 30-40, 40-50. If the median mark of the class is 25, explain how the median helps in understanding the performance of the class. How would the result change if a new student scored 48 marks and was added to the data?
Q2
The average (mean) age of a group of 10 people is 30 years. If one more person joins the group and the new average becomes 32 years, find the age of the new person. Discuss how changes in data points can impact the overall mean and how this can be useful in real-life decision-making.
Q3
In a factory, daily production data over a month is collected and represented as a frequency distribution table. The production manager wants to know if the data is skewed. Explain how you would use statistical measures like mean, median, and mode to determine the skewness of the data, and why understanding skewness is important in analyzing production performance.
NCERT Exemplar Solutions
Questions
1. In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is.
(A) 6 (B) 7 (C) 8 (D) 12
2. The range of the data : 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is
(A) 10 (B) 15 (C) 18 (D) 26
3. The width of each of five continuous classes in a frequency distribution is 5 and the lower class-limit of the lowest class is 10. The upper class-limit of the highest class is.
(A) 15 (B) 25 (C) 35 (D) 40
4. A grouped frequency table with class intervals of equal sizes using 250-270 (270 not included in this interval) as one of the class interval is constructed for the following data : 268, 220, 368, 258, 242, 310, 272, 342, 310, 290, 300, 320, 319, 304, 402, 318, 406, 292, 354, 278, 210, 240, 330, 316, 406, 215, 258, 236. The frequency of the class 310-330 is:
(A) 4 (B) 5 (C) 6 (D) 7
9. A grouped frequency distribution table with classes of equal sizes using 63-72 (72 included) as one of the class is constructed for the following data : 30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96, 102, 110, 88, 74, 112, 14, 34, 44. The number of classes in the distribution will be
(A) 9 (B) 10 (C) 11 (D) 12
10. The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
(A) 28 (B) 30 (C) 35 (D) 38
11. The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be.
(A) 50.5 (B) 51 (C) 51.5 (D) 52
12. In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded : 46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44 Which ‘average’ will be a good representative of the above data and why?
13. The class marks of a continuous distribution are : 1.04, 1.14, 1.24, 1.34, 1.44, 1.54 and 1.64 Is it correct to say that the last interval will be 1.55 - 1.73? Justify your answer.
14. Can the experimental probability of an event be a negative number? If not, why?
15. Mean of 50 observations was found to be 80.4. But later on, it was discovered that 96 was misread as 69 at one place. Find the correct mean.
16. Refer to Q1 above. Construct a grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 - 20 (20 not included).
17. The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table.
| Length (in mm) | Number of leaves |
|---|---|
| 118 - 126 | 8 |
| 127 - 135 | 10 |
| 136 - 144 | 12 |
| 145 - 153 | 17 |
| 154 - 162 | 7 |
| 163 - 171 | 5 |
| 172 - 180 | 3 |
18. The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
Case-Based Questions
Q1
Case: Garden Design
Scenario: A school conducted a survey on the favorite subjects of 100 students. The data collected is as follows:
Mathematics: 30 students , Science: 25 students , English: 20 students , Social Studies: 15 students , Hindi: 10 students
Questions:
1. Represent the data in the form of a bar graph or pie chart.
2. Calculate the mode and explain what it tells you about the students' subject preferences.
Q2
Case: Park Planning
Scenario: The daily temperatures (in degrees Celsius) recorded in a city over 10 consecutive days are as follows: 24, 26, 25, 30, 28, 29, 31, 27, 26, 29.
Questions:
1. Find the mean, median, and mode of the temperatures.
2. Based on the results, analyze the consistency of the temperatures during these 10 days and discuss which measure (mean, median, or mode) gives the most accurate idea of the city's average temperature.