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Statistics Miscellaneous Exercise On Chapter 13 Solutions
- Q1: The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
- Q2: The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.
- Q3: The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
- Q4: Given that $\overline{x}$ is the mean and $\sigma^2$ is the variance of $n$ observations $x_1, x_2, ..., x_n$. Prove that the mean and variance of the observations $ax_1, ax_2, ax_3, ...., ax_n$ are $a\overline{x}$ and $a^2\sigma^2$, respectively, ($a eq 0$).
- Q5(i): The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (i) If wrong item is omitted.
- Q5(ii): The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (ii) If it is replaced by 12.
- Q6: The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.
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"Preparation Methods for Physics Exam" – Class 11 Understand the Syllabus Begin by understanding the entire Class 11 physics syllabus. Identify the topics that carry more weight in the exam and prioritize your study accordingly. Create a study Schedule Plan a realistic study schedule that allows you to cover all topics before the exam. Allocate more time to challenging topics or those you find difficult. Use Quality Study Material: Refer to your textbook, class notes, and any additional reference books recommended by your teacher. Online resources, video lectures, and educational websites can provide additional clarity. Practice Regularly: Practice numerical problems and derivations regularly to enhance your problem-solving skills. Solve sample papers and previous years' question papers to get an idea of the exam pattern. Make Notes: Create concise and organized notes while studying. These notes will be helpful during last-minute revisions. Highlight key concepts, formulas, and important points. Focus on Weak Areas: Identify your weak areas and dedicate more time to understanding and practicing those topics. Seek help from teachers, classmates, or online resources if needed. Time Management: Practice time management while solving sample papers and during self-assessment. Allocate specific time slots for different topics to cover the entire syllabus systematically. Conceptual Understanding Focus on understanding the concepts rather than rote memorization. This will help you in solving application-based questions. If you don't understand a concept, don't hesitate to ask your teacher or seek clarification from other reliable sources Requesting to have a look at my profile for more information
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