10.95 points 2481 points A statistics teacher gave her class a 15 point quiz. Th
ID: 3303320 • Letter: 1
Question
10.95 points 2481 points A statistics teacher gave her class a 15 point quiz. The summary statistics for the students' scores are shown in the table at the right. a. Notice that the median score and the third quartle are the 1. 9.5 12 12 15 same. Explain how this can be. b. One student's parent heaped praise on him for scoring 13, saying it was an amazing score. Comment on whether that praise is deserved using the summary statistics as support To convert these raw scores to a score out of 100, the teacher multiplies each score by six, then adds 10. (We can debate the wisdom of such a strategy later!). What is the median converted score? And the IQR? c. d. What are the mean and standard deviation of the converted test scores? Nickels minted in the United States are supposed to weigh 5.000 grams. Of course there is some variation in that. The actual weights are pretty well represented by a normal model with a mean of 5.000 g and a standard deviation of about 0.08 g. Draw and clearly label this model. 2. Copyright© 2016 Pearson Education, Inc.Explanation / Answer
(a)
When the distribution is skewed to left then distance between the median and third quartile reduces.
(b)
Score 13 is greater than third quartile. That is at least 75% scores are less than 13. So it is a good score.
(c)
Since each score is multiplied by same number and then a same number is added to each score so order of data values remain same.
Median is also multiplied by 6 and added by 10. That is new median will be
median = 12*6 +10 = 82
First quartile: 9.5*6 +10 = 67
Third quartile: 12*6 +10 = 82
IQR : 82 -67 = 15
Old IQR: 12-9.5 = 2.5
That is IQR is also multiplied by 6.
d)
Mean is also mulilied by 6 and then increaed by 10.
New mean: 10.95*6 +10 = 75.7
Standard deviation is also multiplied by 6 but not increased by 10.
That is
SD = 2.481 *6 = 14.886
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