NCERT Solutions for Class 11 Statistics Chapter 8: Use of Statistical Tools

First, choose a topic that interests you and is feasible to research.

1. Problem: I want to understand how much time my classmates spend on digital media (like social media, OTT platforms, and gaming) and how it affects their daily routine.
2. Project Title: "A Survey on the Impact of Digital Media on the Daily Schedule of Class 11 Commerce Students in XYZ Public School, Delhi."
3. Objectives:
   • To determine the average hours spent by students on digital media per day.
   • To identify the most popular digital media platforms.
   • To analyse the perceived impact on study hours and sleep patterns.

Define who you will collect data from.

• Target Population: All 150 students of Class 11 (all streams) in XYZ Public School.
• Sample: It's difficult to survey all 150 students. So, I will use random sampling to select a sample of 30 students (10 from each stream: Science, Commerce, and Arts) to ensure representation.

(Pro-Tip: Conduct a pilot survey with 4-5 friends to check if the questions are clear.)

Once you have the filled questionnaires, it's time to organise the raw data.

Presentation:

• Use a Bar Graph to show the data from Table 1.
• Use a Pie Chart to show the percentage of students using each platform (from Question 2).

• Analysis: From Table 1, we can see that the modal class is 3-5 hours, as it has the highest frequency (12 students). This suggests that a majority of students spend 3-5 hours on digital media. We can also calculate the mean number of hours.
• Interpretation: The data indicates a significant amount of time is dedicated to digital media. For instance, "The analysis reveals that 12 out of 30 students (40%) spend 3-5 hours daily on digital media. Furthermore, 6 students (20%) spend over 5 hours, which is a cause for concern regarding their academic focus."

"The study concludes that digital media usage is high among Class 11 students of XYZ school, with a majority spending over 3 hours daily. Platforms like Instagram and YouTube are most popular. A significant number of students believe it negatively impacts their study time. Therefore, creating awareness about digital wellness is recommended."

• Bibliography:
  1. Statistics for Economics, Class 11, NCERT, 2026-27 Edition.
  2. (Add any other website or book you used).
• Acknowledgement: I would like to express my sincere gratitude to my statistics teacher, [Teacher's Name], for their valuable guidance. I also thank the students who participated in my survey.

A good questionnaire should have:

• A limited number of questions.
• Simple and clear language.
• Questions moving from general to specific.
• No leading or biased questions.
• Clear instructions for the respondent.
• A neat and attractive layout.

• Primary Data: This is first-hand data collected by the investigator for a specific purpose. It is original and more reliable. Methods include surveys, interviews, and observations.
• Secondary Data: This is second-hand data that has already been collected and processed by someone else. It is less expensive and quicker to obtain. Sources include government publications, websites, and research papers.

Defining the target population is crucial because it clarifies the exact group the research is focused on. This ensures that the sample selected is representative of that group, and the conclusions drawn are relevant and accurate for that specific population. Without a clear definition, the survey results can be misleading.

Preparing a statistical project report involves a systematic process. The key steps are:

1. Identification and Statement of the Problem: Clearly define the topic of your study. It should be specific, interesting, and researchable.
2. Objectives of the Study: List what you aim to find out through your research.
3. Choice of Target Group: Identify the total population for your study and select a representative sample from it using an appropriate sampling method (e.g., random or non-random).
4. Collection of Data: Decide whether to use primary or secondary data. For primary data, design a questionnaire or interview schedule. Conduct a pilot survey to test it. Then, collect the data from your chosen sample.
5. Organisation and Presentation of Data: Organise the raw data using tally marks and create frequency distribution tables. Then, present the data visually using bar graphs, pie charts, histograms, or frequency polygons to make it understandable.
6. Analysis and Interpretation: Apply relevant statistical tools like calculating the mean, median, mode, correlation, etc. Explain what the results mean in the context of your objectives.
7. Conclusion: Summarise your key findings. State whether your objectives were met and provide a concluding statement on the problem.
8. Bibliography: List all the books, reports, and websites you referred to.

To conduct a survey on the "lunch preferences of office workers in my locality," I would follow these steps:

1. Define the Scope: My locality is large, so I'll limit my study to 3-4 major office buildings. My target population will be all the workers in these buildings.
2. Sampling: Surveying everyone is impractical. I will use stratified random sampling. I'll select a sample of 50 workers, ensuring a mix of junior and senior employees, and male and female workers.
3. Data Collection (Primary Data):
   • I will design a simple questionnaire with questions like:
     • What is your preferred lunch type? (Home-cooked, Tiffin Service, Office Canteen, Restaurant)
     • What is your average spending on lunch per day? (<₹50, ₹50-₹100, >₹100)
     • What cuisine do you prefer most? (North Indian, South Indian, Chinese, etc.)
   • I'll conduct a pilot survey with 5 workers to refine the questions.
   • I will then approach the 50 selected workers during their lunch break to get the questionnaires filled.
4. Organisation of Data: I will create a master table and use tally marks to create frequency tables for each question.
5. Presentation of Data:
   • I will use a Pie Chart to show the percentage distribution of preferred lunch types (Home-cooked vs. Canteen, etc.).
   • I will use a Bar Graph to show the average spending on lunch.
6. Analysis & Conclusion: I will analyse the data to find trends, e.g., "60% of junior employees prefer the office canteen due to cost, while 50% of senior employees prefer restaurants." My conclusion would summarise these findings.

Q11. What is the primary objective of Rohan's study?
Answer: The primary objective is to find out and analyse the relationship or correlation between the number of self-study hours and the marks obtained by students.

Q12. Which statistical tool is most appropriate for Rohan to use to find the relationship?
Answer: The most appropriate statistical tool is Correlation Analysis (specifically, Karl Pearson's coefficient of correlation).

Q13. Rohan's calculated value is +0.85. What does this value interpret?
Answer: The value +0.85 indicates a strong positive correlation.
- Positive (+): It means that as one variable (study hours) increases, the other variable (marks) also tends to increase.
- Strong (0.85): The value is close to +1, which signifies a very strong linear relationship between the two variables.

Q14. What kind of graph can Rohan use to visually represent this relationship?
Answer: Rohan can use a Scatter Diagram to visually represent the relationship between study hours and marks. Each point on the graph would represent a student's study hours (on the X-axis) and marks (on the Y-axis).

Q15. Is Rohan's data primary or secondary? Justify your answer.
Answer: Rohan's data is primary data. This is because he collected it himself, directly from his classmates, for his specific research purpose. He did not use any pre-existing source.