ASSIGNMENT 2 Q.1) Directions: For each of these questions, choose the option (a, b, C or d) that is TRUE and give a justification on why you chose that answer. 1. If in a discrete series 85% values are less than 30, then it describes what value a. 𝑃30 = 85 b. 𝑄1 = 30 c. 𝐷85 = 75 d. 𝑃85 = 30 2. If the coefficient of variation for prices is 5.483% and the mean price is Rs 15.5, then the variance price 𝑅𝑠 2 is equal to a. 0.85 b. 84.9865 c. 28.269 d. 0.7225 3. Through visualization not mathematically determine the location of mean, median and mode classes from the given Histogram of Prices of 300 cars. a. 𝑀𝑒𝑎𝑛 = 1.449 − 1.995, 𝑚𝑒𝑑𝑖𝑎𝑛 = 1.995 − 2.495, 𝑚𝑜𝑑𝑒 2.495 − 2.995 b. 𝑀𝑒𝑎𝑛 = 1.449 − 1.995, 𝑚𝑒𝑑𝑖𝑎𝑛 = 2.495 − 2.995, 𝑚𝑜𝑑𝑒 1.995 − 2.495 c. 𝑀𝑒𝑎𝑛 = 2.995 − 3.495, 𝑚𝑒𝑑𝑖𝑎𝑛 = 2.495 − 2.995, 𝑚𝑜𝑑𝑒 1.995 − 2.495 d. 𝑀𝑒𝑎𝑛 = 1.995 − 2.495, 𝑚𝑒𝑑𝑖𝑎𝑛 = 1.995 − 2.495, 𝑚𝑜𝑑𝑒 1.995 − 2.495 = = = = 4. The mean marks got by 68 students in the subject of Statistics are 65. The mean of the top 10 of them was found to be 80 and the mean of the last 10 was known to be 50. The mean of the remaining 48 students is determined by a. 60 b. 65 c. 0 d. 48 5. Which of the following statement is not a property of the standard deviation? a. It is always negative number b. It is affected by extreme values in a data set c. It is based on all the values in the data set d. It is the most widely used measure of dispersion 6. The following data represent the numbers of minor penalties accrued by each of the 30 National Hockey League franchises during the 2007–08 regular season. 318 378 405 336 381 409 337 384 417 339 385 431 362 386 433 363 387 434 366 390 438 369 393 444 372 395 461 375 403 480 The 8th Decile penalties of League will be determined as a. 431 b. 417 c. 433 431+433 d. 2 7. Geometric mean and harmonic mean for the values 3, -11, 0, 63, -14, 100 are a. 0 and 3 b. 3 and -3 c. 0 and 0 d. Infinite and impossible 8. Which of the following is the mean of the squared deviations of x values from the mean? a. Mean deviation from mean b. Variance c. Standard error d. Standard deviation 9. The mean of 20 values calculated as 312.6452. which of the following is always true? a. ∑(𝑋 − 312.6452) = 20 b. ∑(𝑋 − 312.6452) ≥ 20 c. ∑(𝑋 − 312.6452) = 0 d. ∑(𝑋 − 312.6452) ≤ 0 10. In a study of distances travelled to a college by commuting students, data from 100 commuters yielded a mean of 8.73 miles. After the mean was calculated, data came in late from three students, with respective distances of 11.5, 7.6, and 10.0 miles. Calculate the mean distance for all 103 students. a. 8.73 b. 9.021 c. 37.83 d. 8.75 11. Refer to the graph below Frequency Polygone 139 120 83 52 32 1 64 0 67 9 70 3 73 76 79 82 85 88 2 91 A. Mode weight is a. 78.9 b. 82 c. 80.5 d. 80 B. Median weight is a. 78.9 b. 82 c. 80.5 d. 80 C. Is this data skewed in any direction? a. Yes, positively skewed c. No, symmetrical b. Yes, negatively skewed d. Not symmetrical nor skewed 12. Consider the following two data sets. Data Set I 12 25 37 8 41 Data Set II 19 32 44 15 48 Notice that each value of the second data set is obtained by adding 7 to the corresponding value of the first data set. The mean and standard deviation for Data Set I is 24.6 and 14.6389 respectively. Then the mean and variance for Data Set II is equal to a. b. c. d. Mean = 24.6 and Variance = 214.3 Mean = 31.6 and Variance = 14.6389 Mean = 31.6 and Variance = 214.3 Mean = 24.6 and Variance = 14.6389 13. If the coefficient of variation for prices is 5.483% and the variance price 𝑅𝑠 2 0.7225 then mean is equal to a. 1.3177 b. 15.5 c. 7.5889 d. 0.5483 14. Through visualization not mathematically determine the location of mean, median and mode classes from the given Histogram. a. 𝑀𝑒𝑎𝑛 = 10.3, 𝑚𝑒𝑑𝑖𝑎𝑛 = 10.1, 𝑚𝑜𝑑𝑒 = 10.1 b. Mean = 10.01, median = 10.2, mode = 10.1 c. 𝑀𝑒𝑎𝑛 = 10.0, 𝑚𝑒𝑑𝑖𝑎𝑛 = 10.2, 𝑚𝑜𝑑𝑒 = 10.1 d. 𝑀𝑒𝑎𝑛 = 10.3, 𝑚𝑒𝑑𝑖𝑎𝑛 = 10.2, 𝑚𝑜𝑑𝑒 = 10.2 15. On a 300-mile auto trip, Lisa covered 52 mph for the first 100 miles, 65 mph for the second 100 miles, and 58 mph for the last 100 miles. The average speed covered by Lisa for the trip equals to a. 59 b. 58.09 c. 58.33 d. 57.85 16. A small country bought oil from three different sources in one week, as shown in the following table. Source Barrels Purchased. Price per Barrel ($) Mexico 1000 51 Kuwait 200 64 Spot Market 100 70 The mean price per barrel for all 1300 barrels of oil purchased in that week equals to a. 61.667 b. 433.33 c. 54.46 d. 64 17. Calculate The following data represent the numbers of minor penalties accrued by each of the 40 National Hockey League franchises during the 2007–08 regular season. 1.6 3.3 4.4 1.9 3.4 4.5 2.2 3.4 4.7 2.5 3.4 4.7 2.6 3.5 2.6 3.5 2.9 3.6 3.0 3.7 3.0 3.7 3.1 3.7 3.1 3.8 3.1 3.8 3.1 3.9 3.2 3.9 3.2 4.1 The 9th Decile penalties of League will be determined as a. 4.3 b. 4.4 4.3+4.4 c. 2 d. 4.2+4.3 2 3.2 4.1 3.3 4.2 3.3 4.3 18. If the three observations are a = 2, b = - 2 and c = 2 then their geometric mean will be: a. 2 b. 0 c. infinite d. – 2 19. The following data give the numbers of times 10 persons used their credit cards during the past 3 months. Mean deviation from mean is equal to 9 6 28 14 2 18 7 3 16 6 a. 0 b. 64.8 c. 6.48 d. 10 20. In a study of speed of a car covered a distance travelled to a college by a student, a harmonic mean yielded 16.7442 miles/ hour. After the mean was calculated that one value of 16 misprinted mistakenly and true value was 10. Then the true Harmonic mean is equal to. a. 10.7442 b. 13 c. 15.7442 d. 13.846 21. The Box and Whisker Plots for the weights (Pounds) and height (inches) of 482 applicants for admission in a cadet college at 2014 are given below Which of the following is an accurate comparison of the box plots? a. On both plots, the median is exactly half way between the Lower and Upper Quartiles. (Yes or No) b. Weights of cadets has a smaller range & heights of cadets has a larger IQR (Inter Quartile Range = 𝑄3 − 𝑄1) (Yes or No) c. Inter Quartile Range of weights of cadets is equal to _____________ and Inter Quartile Range of heights of cadets is equal to ___________ 22. Consider the following two data sets. Data Set I: 4 8 15 9 11 Data Set II 8 16 30 18 22 Notice that each value of the second data set is obtained by multiplying the corresponding value of the first data set by 2. The mean and variance of Data Set I is calculated as 9.4 and 4.03732 respectively. The mean and variance of Data Set II will be equal to a. Mean = 2 × 9.4 and Variance = 4.03732 b. Mean = 2 × 9.4 and Variance = 2 × 4.03732 c. Mean = 2 × 9.4 and Variance = 4 × 4.03732 d. Mean = 4 × 9.4 and Variance = 4 × 4.03732 23. Refer to the graph below Frequency polygone 175 158 62 1 0.395 55 5 0.615 0.835 1.055 1.275 1.495 8 13 1.715 1.935 0 2.155 1 2.375 1 2.595 A. Mode expense rate is a. 0.835 b. 1.055 c. 1.275 d. 0.945 B. Median expense rate is a. 0.835 b. 1.055 c. 1.275 d. 0.945 C. Is this data skewed in any direction? a. Yes, positively skewed c. No, symmetrical b. Yes, negatively skewed d. Not symmetrical nor skewed Q.2 Short questions 1. Two data sets of weights (Pounds) of 469 and 478 applicants for admission in a cadet college at 2012 and 2013 respectively are given below 1. Find the missing values in the table below. Class Mean Variance Median Q1 Q3 Minimum Maximum 2012 2013 219.7741 26.5871 219.3646 26.2187 2. Indicate the skewness or symmetry for both classes. Which class contains outlier(S). Identify it? 3. Indicate in which year the cadets have more homogenous weights? 2. The histogram and excel outcome of descriptive statistics of ten Year return for funds of 479 retired police officers for year 2016 are given below Column1 Mean Standard Error Median Mode 7.217870564 0.082967258 7.31 8.89 Bin / upper class limits 0.3 1.71 3.12 4.53 Frequency Cumulative % 1 4 5 16 0.21% 1.04% 2.09% 5.43% Standard 1.81582711 Deviation Sample Variance 3.297228092 Kurtosis 1.448602426 Skewness 0.458405475 Range 14.1 Minimum -1.1 Maximum 13 Sum 3457.36 Count 479 5.94 82 22.55% 7.35 8.76 138 147 51.36% 82.05% 10.17 65 95.62% 11.58 12.99 14.4 More 17 3 1 0 99.16% 99.79% 100.00% 100.00% 1. Complete a frequency distribution and draw a histogram for a given frequency distribution 2. Detect any outlier (s) in this data set if it exist in your opinion 3. Find a better summary measure of central tendency whether it is the mean or the median? Explain. 4. Identify the symmetry and skewness of 10 year returns of 479 officers. 5. Find the (approximate) value of the 95th percentile. Give a brief interpretation of this percentile. 6. Indicate is there any consistency in 10 year returns of 479 officers? 7. Find the percentages of the given data values that fall within 1.5 standard deviation of the mean. (𝑋̅ ± 1.5 𝑆. 𝐷) 3. The geometric mean of four numbers were calculated as 107.8482. After it was noted that the third value 111.3 wrongly considered instead of 110.25 value. Find the true geometric mean? 4. A man travels by a car for 4 days. He travelled for 10 hours each day. He drove on the first day at the rate of 45 km per hour, second day at 40 km per hour, third day at the rate of 38 km per and the fourth day at the rate of 37 km per hour. Which average , harmonic mean or arithmetic mean or geometric mean will give average speed? why? 5. A sample of restaurants in a large city revealed that the average price of a cup of coffee was 58 cents, and the standard deviation was 8 cents. Three of the restaurants charged 50, 45, and 60 cents. Find Z-scores for these restaurants. 6. Jane works for a company whose employees had an average income this past year of $28,000 with a standard deviation of $3000. How much did Jane earn this past year if her z-score is -0.8? 7. In a marketing experiment a supermarket chain of three stores sold lettuce, on a certain day, at a different price in each of its stores. Store Head Price (cents) 1 75 98 2 125 88 2 300 69 a. How much was the average price per head of lettuce sold by the supermarket chain? b. How many additional heads of lettuce must be sold at 98 cents a head to raise the mean price of lettuce sold that day by the supermarket chain to 80 cents per head ? 8. The histogram and excel outcome of descriptive statistics of Assets for funds of 479 retired police officers for year 2016 are given below Column1 Mean 1644.716305 Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 128.1842876 547.73 779.93 2805.450115 7870550.35 9.85459805 2.968398968 19384.17 4.13 19388.3 787819.11 479 Bin / upper class limits 1942.546 3880.963 5819.38 7757.797 9696.214 11633.631 13572.048 15510.465 17448.882 19387.29 21325.707 More Frequency Cumulative % 371 57 13 10 14 3 5 5 0 0 1 0 77.45% 89.35% 92.07% 94.15% 97.08% 97.70% 98.75% 99.79% 99.79% 99.79% 100.00% 100.00% 1. Complete a frequency distribution and draw a histogram for a given frequency distribution 2. Detect any outlier (s) in this data set if it exist in your opinion 3. Find a better summary measure of central tendency whether it is the mean or the median? Explain. 4. Identify the symmetry and skewness of this data. 5. Find the (approximate) value of the 97th percentile. Give a brief interpretation of this percentile. 6. Indicate is there any homogeneity of Assets for funds of 479 retired police officers for year 2016? 9. One Year return for funds of 479 retired police officers for year 2016 collected and this information has been summarised on the box plots below. 1. Describe the five number value summary 2. Is the data set skewed in any direction? If yes, detect it as skewed to the right or to the left? Does this data set contain any outliers? If yes then identify it. 10. The histogram and excel outcome of descriptive statistics of heights (inches) of 439 applicants for admission in a cadet college at 2000 are given below Bin / Cumulative Heights (Inches) upper Frequency % class limits Mean 78.93849658 65 2 0.46% Standard Error 0.18088487 68 0 0.46% Median 79 71 8 2.28% Mode 81 74 50 13.67% Standard 3.789958918 77 84 32.80% Deviation Sample Variance 14.3637886 80 117 59.45% Kurtosis 0.516420999 83 142 91.80% Skewness -0.395616882 86 30 98.63% Range 28 89 4 99.54% Minimum 63 92 2 100.00% Maximum 91 More 0 100.00% Sum 34654 Count 439 1. Complete a frequency distribution and draw a histogram for a given frequency distribution 2. Detect any outlier (s) in this data set if it exist in your opinion 3. Find a better summary measure of central tendency whether it is the mean or the median? Explain. 4. Identify the symmetry and skewness of this data. 5. Find the (approximate) value of the 95th percentile. Give a brief interpretation of this percentile. 6. Indicate is there any homogeneity in heights of 439 cadets? 11. How much does the typical American family spend on average to go away on vacation each year? Twenty-five randomly selected households reported the following vacation expenditures (rounded to the nearest hundred dollars) during the past year: 2500 500 800 0 100 0 200 2200 0 200 0 1000 900 321,400 500 500 100 0 8200 900 0 1700 1100 600 3400 a. Find mean, median and mode of given data. b. Label the best measure of central tendency to answer the original question? 12. The histogram and excel outcome of descriptive statistics of heights (Inches) of 441 applicants for admission in a cadet college at 2014 are given below Column1 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 78.95464853 0.180517434 79 81 3.790866107 14.37066584 0.228646046 -0.354535468 28 63 91 34819 441 Bin / upper class limits 65 68 71 74 77 80 83 86 89 92 More Frequency 1 0 9 52 83 120 139 32 3 2 0 Cumulative % 0.23% 0.23% 2.27% 14.06% 32.88% 60.09% 91.61% 98.87% 99.55% 100.00% 100.00% 1. Complete a frequency distribution and draw a histogram for a given frequency distribution 2. Detect any outlier (s) in this data set if it exist in your opinion 3. Find a better summary measure of central tendency whether it is the mean or the median? Explain. 4. Identify the symmetry and skewness of this data. 5. Find the (approximate) value of the 90th percentile. Give a brief interpretation of this percentile. 6. Indicate is there any homogeneity in heights of 441 cadets? 7. Find the percentages of the given data values that fall within 0.5 standard deviation of the mean. (𝑋̅ ± 0.5 𝑆. 𝐷) The End SUBMISSION DATE 04/04/2022