Statistics Midterm Question Answers UIU-MSCSE.pdf
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📝 File Description Summary 📄 Statistics Midterm Question Answers - UIU MSCSE This PDF contains the midterm exam questions and answers for the Statistics course in the Master of Science in Computer Science & Engineering (MSCSE) program at United International University (UIU). It includes a variety of solved problems covering probability, hypothesis testing, distributions, statistical measures, and more. Ideal for students preparing for exams or reviewing statistical concepts. ✅ Clear formatting 📚 Comprehensive solutions 🎓 Tailored for UIU MSCSE students
Statistics Midterm Question Answers UIU-MSCSE.pdf
- 1. 1. Consider the following frequency distribution of CGPA of 100 UIU students. CGPA 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 No of students 7 18 35 27 10 3 (a).Sketch histogram and frequency polygon of the frequency distribution in the same graph. Also, sketch the pie chart. (b).Sketch histogram and find the mode from it. Check your result. (c).Draw the cumulative frequency curve (OGIVE) and find median, 3rd quartile, 7th Decile, and 55th Percentile from the OGIVE. Also, verify by the analytical method. (d).Find arithmetic mean and standard deviation of the frequency distribution. (e).Find the statistical index for the value 𝑥 = 2.6. (f). Estimate median and then mean deviation from median. Also, find the coefficient of the mean deviation. (g).Find first four raw moments about 𝐴 = 1.75 and convert them to the central moments. 2. Each member of an athletics club was asked to monitor the distance run in training during a particular week. The table below summarizes the results. Distance to nearest Km 30-40 40-50 50-60 60-70 70-80 80-90 Number of athletes’ 2 4 7 12 9 6 (a).Find the cumulative frequency polygon. (b).Estimate 𝑄1, 𝑀𝑒, 𝐷6, and 𝑃85 from the cumulative frequency polygon. (c).Estimate the mean distance and the standard deviation of the distribution. (d).Find the interquartile range of the given distribution. 3. The frequency distribution table of CGPA of the some UIU students is given below. CGPA 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 Frequency 4 18 a 25 9 5 Cumulative frequency 4 22 51 b 85 90 (a).Find the values of 𝑎 & 𝑏 to complete the frequency distribution table. (b).Find the median class and hence find the percentage of the frequency of that class. 4. The following table shows the results of a survey to find the average daily time, in minutes, that a group of children spent in internet chat rooms, where the mean time was estimated to be 27.5 minutes. From an equation involving 𝑓 and hence show that the total number of children in the survey was 26. Time per day 0-10 10-20 20-40 40-80 No of children 2 𝑓 11 4
- 2. 5. If the mode of the following frequency table is 2.34, find the unknown frequency 𝑓. Hence, find the statistical index (standardized value) of 𝑥 = 2.75. CGPA 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 No of students 7 18 35 𝑓 10 3 6. From the following frequency polygon construct the corresponding frequency table and hence find the standardized value for 𝑥 = 60. 7. From the following cumulative frequency polygon construct the corresponding frequency table and hence find the geometric and harmonic mean of the distribution.
- 3. 8. Consider the total 200 students with the age ranges as follows. Construct the corresponding frequency distribution table. 9. From the following histogram construct the corresponding frequency table. Find the median and corresponding mean deviation of the distribution.
- 4. 10. In a class of 35 students the CGPA of the class are summarized as the sums ∑ 𝑓𝑖𝑥𝑖 = 112 and ∑ 𝑓𝑖𝑥𝑖 2 = 562. Find their mean and standard deviation. 11. A summary of 24 observations of 𝑥 is given as the sums ∑ 𝑓𝑖(𝑥𝑖 − 𝑎) = −73.2 and ∑ 𝑓𝑖(𝑥𝑖 − 𝑎)2 = 2215, where the mean of these observations is 8.95. (a).Find the value of the constant 𝑎. (b).Find the standard deviation of 𝑥. 12. In a certain factory there are four working groups and they need 3, 4, 5, and 2 hours per product to make. What is the approximate average time required to make a product by those groups? 13. Let the class marks of a certain population table are 17, 22, 27, 32, and 37 and the corresponding frequencies are 9, 13, 8, 10, and 15. (a).Determine size of the classes and hence construct the original classes. (b).Find the median class and hence find the percentage of the frequency of that class. (c).Find the sample size. 14. The cumulative distribution polygon of visits of calculus tutorial portal is given below.
- 5. (a).Construct the frequency distribution table and hence find the geometric mean. (b).Find the median of visits from the graph. (c).Find the standard deviation of the frequency distribution. (d).Find the inter-quartile range from the graph. (e).Sketch the histogram and hence the mode of the visits. (f). Find the percentage of visits between 7 to 21 visits? 15. There are three groups of people have average earnings $150, $170, and $140 respectively. If the first two groups contain 17 and 12 people respectively and the combined average of earnings is $153.25, find the number of people in the last group. 16. If the mode of a certain frequency table is 65.5 and the lower limit of the modal class is 60.5 with the class size 10, find the frequency of the modal class. Here frequency difference of the modal class and pre-modal class is 7 and frequency of post-modal class is 14. 17. If the standard deviation of a frequency table is 3.6 and coefficient of standard deviation is 6.55%, find the arithmetic mean of that table. 18. The cumulative frequency graph illustrates the height of 200 students in a community. (a).State the range of the data. (b).Construct a box and whisker plot to illustrate the data. (c).What percentage of students have height more than 170 cm? (d).Find the position of the height of 40th percentile and 70th percentile. (e).Find the outlier if there exits any.
- 6. 19. The birth weights of random samples of 900 babies born in country 𝐴 and 900 babies born in country 𝐵 are illustrated in the cumulative frequency graphs. Use suitable data from these graphs to compare the central tendency and spread of the birth weights of the two sets of babies. 20. For the following Cumulative Frequency Polygon construct a Box-Whisker plot.
- 7. 21. Distributions of the shopping time (in minutes) for two groups of people are given in the following Box-Whisker plot. (a).Find inter-quartile range (IQR) and hence investigate the consistency of the shopping time for the target groups. (b).Describe the nature (skewness) of the distributions. 22. Analyze the following dual Box-Whisker plot. You may comment about the central tendency, consistency, skewness, and kurtosis. 23. For the following Box-Whisker plot find the appropriate central tendency and check the consistency of the given samples.
- 8. 24. According to the following Box-Whisker plot write the relation among the Mode, Median, and Mean. 25. Compare the data sets represented through the Box-Whisker plots given below. 26. Consider the following frequency distribution of CGPA of 100 UIU students. CGPA 1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 No of students 7 18 35 27 10 3 (a).Find first four raw moments about 𝐴 = 1.75 and convert them to the central moments. (b).Find the co-efficient of skewness and co-efficient of kurtosis. (c).Comment on your findings. 27. Suppose the first four raw moments of a population are −3.7, 94, −547.2, and 1200 respectively. (a).Find the first four central moments. (b).Estimate the coefficient of skewness and kurtosis. (c).Show your result graphically and comment about your findings.
- 9. 28. If co-efficient of skewness and kurtosis of a frequency distribution are −0.95 and 4.32, respectively. Explain the shape of the distribution. 29. Discuss the strength of correlation from the following Pearson’ correlation coefficient. (i) 𝑟 = −0.15 (ii) 𝑟 = −1 (iii) 𝑟 = 0.65 (iv) 𝑟 = 1 (v) 𝑟 = 0 30. Consider ∑ 𝑥 = 360, ∑ 𝑥2 = 9802, ∑ 𝑦 = 345, ∑ 𝑦2 = 8469, and ∑ 𝑥𝑦 = 8238 for 15 observations of 𝑥 and 𝑦. (a).Find the coefficients 𝑏𝑦 𝑥 and 𝑏𝑥 𝑦 and hence estimate 𝑟𝑥𝑦. (b).Find and sketch the regression line of 𝑥 on 𝑦. (c).Graphically determine 𝑥 for 𝑦 = 25. 31. For the following data find the correlation co-efficient. How much 𝑦 depends on 𝑥? Also, find the corresponding regression line. 𝑥 5 12 18 23 27 30 26 22 𝑦 18 16 13 11 9 7 10 13 32. Fit a least-squares line to the following set of data by using 𝑥 as the dependent variable. Also, from the graph of least-squares line predict 𝑥 for 𝑦 = 11. 𝑥 1 3 4 6 8 9 11 14 𝑦 1 2 4 4 5 7 8 9 33. A department store has the following statistics of sales (𝑌) for a period of 2 years of 10 salespersons who have varying years of experience (𝑋) in sales promotion. Experience (𝑋) in Years 1 3 4 4 6 8 10 10 11 13 Average Annual sales (𝑌) in thousand 80 97 92 102 103 111 119 123 117 136 (a).Using the above set of data calculate the value of 𝑟 (coefficient of correlation) and interpret the result. (b).Find the regression line of 𝑌 on 𝑋 in the form 𝑌 = 𝑎 + 𝑏𝑋. (c).Sketch a scatter diagram in Years (𝑋) vs Average Annual sales (𝑌). (d).Verify your model found in question (b) with the tabular value for 6 years’ experience. (e).Predict the annual sales volume of persons what have 12 and 15-years’ experience. (f). Indicate why it may not be appropriate to use your question to predict the average annual sales at 30 years of experience. 34. If the correlation coefficient of 𝑥 & 𝑦 is 0.75 and the corresponding standard deviations 1.25 & 1.75. Find the regression coefficient of 𝑦 on 𝑥 and 𝑥 on 𝑦.
- 10. 35. If the correlation coefficient of two variables is 0.72 and regression coefficient of 𝑥 on 𝑦 is 1.08. If 𝑥̅ = 29.2 and 𝑦 ̅ = 37.5 find the regression line of 𝑦 on 𝑥. Also, find the value of 𝑦 when 𝑥 = 44 graphically. 36. If the correlation coefficient of two variables is 0.65 and regression coefficient of 𝑦 on 𝑥 is 1.68. Also, 𝑥̅ = 32.3 and 𝑦 ̅ = 45.6. (a).Find the regression coefficient of 𝑥 on 𝑦. (b).Find and sketch the regression line 𝑥 on 𝑦. (c).Predict the value of 𝑥 when 𝑦 is 52. Also, verify your result graphically. 37. Find the rank correlation co-efficient between obtained places of 8 students in Mathematics and Physics. Serial 1 2 3 4 5 6 7 8 Mathematics 3 1 6 5 7 4 8 2 Physics 8 3 1 2 6 5 4 7 38. Ten candidates were ranked as follows by two independent examiners, according to the score they obtained in an interview. Calculate the Spearman’s rank correlation coefficient and interpret the result. Candidate Number 1 2 3 4 5 6 7 8 9 10 Ranked by Ex. 1 7 9 1 3 8 4 10 5 6 2 Ranked by Ex. 2 9 5 1 4 6 7 8 2 10 3