#$&* course MTH 152 Time: 4:22PM Date: 7/29 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `aThe numbers, in order, are .1, .2, .3, .3, .4, .5, .6, .7, .8, .9, .9 The mean, obtained by adding the 11 numbers then dividing by 11, is .518. The median occurs at position (n + 1 ) / 2 = 6 in the ordered list. This number is .5. Note that there are five numbers before .5 and five numbers after .5. The maximum number of times a number repeats in this distribution is 2. So there are two modes (and we say that the distribution is bimodal). The modes are .3 and .9. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): - Easy stuff, only hard part is not going cross-eyed with all the commas and decimals. Expect extra spaces in my sets of numbers to preserve sanity. - Additional Inquiry = consider my definition of “mode” and provide any comments/insight as necessary.
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Given Solution: `aThe mean is drastically affected by the error; correcting the error changes the mean by about 3 units. The median number, however, simply shifts 1 position, changing from 2.28 to 2.39. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query problem 13.2.30 Salaries 6 @$19k, 8 @ 23k, 2 @ 34.5k, 7 @ 56.9k, 1 @ 145.5k. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: - I experiment with combining the number of employees / salaries as follows - (6*$19k, 8 * $23k, 2 *$34.5k, 7 * $56.9k, 1 * 145.5k ) - Taking the product of number of employees * salary - (114, 184, 69, 398.3, 145.5) = 841.8 - Taking the quotient of the total salary and the average number of employees in question, - (6, 8, 2, 7, 1) = 24 = 841.8 / 24 = 35.075 - Following the constraint listed in the text to round to the nearest hundred dollars, the mean salary is $35.1K confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aIF THERE ARE 28 EMPLOYEES: The totals paid for each salary level are: 6 * $19,500 = $117,000 8 * $23,000 = $184,000 4 * $28,300 = $113,200 2 * $34,500 = $69,000 7 * $36,900 = $258,300 1 * $145,500 = $145,500 The grand total paid in salaries to the 28 employees is therefore $887,000, giving an average of $887,000 / 28 = $31,700. The median occurs at position (n + 1) / 2 = (28 + 1) / 2 = 14.5. Since the 14 th salaray on a list ordered from least to greatest is $23,000 and the 15 th is $28300 the median is ($23000 +$28300) / 2 = $25,650. The mode is 23,000, since this salary occurs more frequently than any other. IF THERE ARE 24 EMPLOYEES: The totals paid for each salary level are: $19,000 * 6 = $114,000 $23,000 * 8 = $184,000 $34,500 * 2 = $69,000 $56,900 * 7 = $398,300 $145,500 * 1 = $145,500 Adding these gives a ‘grand total’, which is divided by the number 24 of employees to obtain the mean $37,950. The median occurs at position (n + 1) / 2 = (24 + 1) / 2 = 12.5. Since the $23000 salary covers positions 7 thru 14 in an ordered lise of salaries the median is $23,000. The mode is 23,000, since this salary occurs more frequently than any other. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): - My mathematical instincts are becoming sharper. I came very close this time, construed only in execution. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query problem 13.2.51 mean, med, mode of 0, 1, 3, 14, 14, 15, 16, 16, 17, 17, 18, 18, 18, 19, 20 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: - Nice how the numbers are organized thusly. - Mean is 206/15 = 13.73 - Median is (n+1)/2 = (15+1)/2 = 8th position, the second 16. - Mode is 3, 18 occurred three times. (Also 14, 16, and 17 occurred twice) confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe mean is 13.73, obtained by adding together all the numbers and dividing by n = 15. The median is in position (n+1) / 2 = (15+1)/2 = 8 on the ordered list; the 8 th number is 16. The mode is 18, which is the only number occurring as many as 3 times. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Okay. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment - Interesting to put the (n+1)/2 position of median equation (hereafter known as POM equation) to use. - Surprising to see how cross-eyed one gets when staring at numerous decimals in a set. - I believe my method of creating “sets” of numbers is handy, especially when running into errors like accidently combining two different sets of numbers with each other. Hopefully this is better prevented by denoting each set as set ‘A, B, C’ and so on. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment - Interesting to put the (n+1)/2 position of median equation (hereafter known as POM equation) to use. - Surprising to see how cross-eyed one gets when staring at numerous decimals in a set. - I believe my method of creating “sets” of numbers is handy, especially when running into errors like accidently combining two different sets of numbers with each other. Hopefully this is better prevented by denoting each set as set ‘A, B, C’ and so on. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!