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Frequency distribution
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5.82. Table 5-16 shows a frequency distribution of the lifetimes of 400 radio tubes tested at the L & M Tube Company. With reference to this table, determine the (a) upper limit of the fifth class (b) lower limit of the eighth class (c) class mark of the seventh class
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Table 5-16
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Lifetime (hours) 300 399 400 499 500 599 600 699 700 799 800 899 900 999 1000 1099 1100 1199 TOTAL Number of Tubes 14 46 58 76 68 62 48 22 6 400
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CHAPTER 5 Sampling Theory
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(d) class boundaries of the last class (e) class interval size (f ) frequency of the fourth class (g) relative frequency of the sixth class (h) percentage of tubes whose lifetimes do not exceed 600 hours (i) percentage of tubes with lifetimes greater than or equal to 900 hours ( j) percentage of tubes whose lifetimes are at least 500 but less than 1000 hours
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5.83. Construct (a) a histogram, (b) a frequency polygon corresponding to the frequency distribution of Problem 5.82. 5.84. For the data of Problem 5.82, construct (a) a relative, or percentage, frequency distribution, (b) a relative frequency histogram, (c) a relative frequency polygon. 5.85. Estimate the percentage of tubes of Problem 5.82 with lifetimes of (a) less than 560 hours, (b) 970 or more hours, (c) between 620 and 890 hours. 5.86. The inner diameters of washers produced by a company can be measured to the nearest thousandth of an inch. If the class marks of a frequency distribution of these diameters are given in inches by 0.321, 0.324, 0.327, 0.330, 0.333, and 0.336, find (a) the class interval size, (b) the class boundaries, (c) the class limits. 5.87. Table 5-17 shows the diameters in inches of a sample of 60 ball bearings manufactured by a company. Construct a frequency distribution of the diameters using appropriate class intervals.
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Table 5-17
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0.738 0.728 0.745 0.733 0.735 0.732 0.729 0.737 0.736 0.730 0.732 0.737 0.743 0.736 0.742 0.732 0.735 0.731 0.740 0.735 0.740 0.730 0.727 0.746 0.736 0.724 0728 0.739 0.734 0.735 0.741 0.733 0.738 0.734 0.732 0.735 0.735 0.742 0.725 0.738 0.736 0.729 0.731 0.736 0.733 0.739 0.741 0.734 0.726 0.739 0.734 0.727 0.736 0.730 0.737 0.735 0.732 0.735 0.744 0.740
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5.88. For the data of Problem 5.87, construct (a) a histogram, (b) a frequency polygon, (c) a relative frequency distribution, (d) a relative frequency histogram, (e) a relative frequency polygon. 5.89. From the results in Problem 5-88, determine the percentage of ball bearings having diameters (a) exceeding 0.732 inch, (b) no more than 0.736 inch, (c) between 0.730 and 0.738 inch. Compare your results with those obtained directly from the raw data of Table 5-17. 5.90. Work Problem 5.88 for the data of Problem 5.82.
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Computation of mean, standard deviation, and moments for samples
5.91. A student received grades of 85, 76, 93, 82, and 96 in five subjects. Determine the arithmetic mean of the grades. 5.92. The reaction times of an individual to certain stimuli were measured by a psychologist to be 0.53, 0.46, 0.50, 0.49, 0.52, 0.53, 0.44, and 0.55 seconds. Determine the mean reaction time of the individual to the stimuli. 5.93. A set of numbers consists of six 6s, seven 7s, eight 8s, nine 9s, and ten 10s. What is the arithmetic mean of the numbers
CHAPTER 5 Sampling Theory
5.94. A student s grades in the laboratory, lecture, and recitation parts of a physics course were 71, 78, and 89, respectively, (a) If the weights accorded these grades are 2, 4, and 5, respectively, what is an appropriate average grade (b) What is the average grade if equal weights are used 5.95. Three teachers of economics reported mean examination grades of 79, 74, and 82 in their classes, which consisted of 32, 25, and 17 students, respectively. Determine the mean grade for all the classes. 5.96. The mean annual salary paid to all employees in a company was $5000. The mean annual salaries paid to male and female employees of the company were $5200 and $4200, respectively. Determine the percentages of males and females employed by the company. 5.97. Table 5-18 shows the distribution of the maximum loads in short tons (1 short ton 2000 lb) supported by certain cables produced by a company. Determine the mean maximum loading using (a) the long method, (b) the coding method.
Table 5-18
Maximum Load (short tons) 9 9.7 9.8 10.2 10.3 10.7 10.8 11.2 11.3 11.7 11.8 12.2 12.3 12.7 12.8 13.2 TOTAL Number of Cables 2 5 12 17 14 6 3 1 60 x f 462 98 480 75 498 56 516 42
Table 5-19
534 30 552 21 570 15 588 11 606 6 624 2
5.98. Find x for the data in Table 5-19 using (a) the long method (b) the coding method. # 5.99. Table 5-20 shows the distribution of the diameters of the heads of rivets manufactured by a company. Compute the mean diameter.
Table 5-20
Diameter (inches) 0.7247 0.7249 0.7250 0.7252 0.7253 0.7255 0.7256 0.7258 0.7259 0.7261 0.7262 0.7264 0.7265 0.7267 0.7268 0.7270 0.7271 0.7273 0.7274 0.7276 0.7277 0.7279 0.7280 0.7282 TOTAL Frequency 2 6 8 15 42 68 49 25 18 12 4 1 250
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