Linear Transformations

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Questions

• If you were to add 5 to each value in a data set, what effect would this have on the standard deviation of the data set?
• If you were to multiply each value in a data set by 6, what effect would this have on the mean of the data set?
• If you were to multiply each value in a data set by 6, what effect would this have on the standard deviation of the data set?
• In a biology lab, a student has measured the lengths of 30 palmetto bugs in inches. He computes the mean and standard deviation as 4.1 inches and 1.2 inches, respectively. He later finds out that he was supposed to calculate the mean and standard deviation in centimeters instead of in inches. What are the new mean and standard deviation of his sample, in centimeters? (Note: 1 in = 2.54 cm)
• A professor's final exam has a mean of 60 and a standard deviation of 12. She decides that it was too difficult, so she adds 15 points to each student's score. Rather than recalculate the mean and standard deviation for the 442 scores, she remembers that she can use the linear transformation rules to recalculate the mean and standard deviation. What are the revised mean and standard deviation of her final exam?
• A meteorologist has recorded daily high temperatures for the last month, in degrees Centigrade, and he presents the mean of 21 degrees C. and standard deviation of 3 degrees C. during the evening news. While on camera, his co-anchor says that nobody understands degrees C, so he does an on-the-spot conversion of these two values to degrees Fahrenheit. What are the converted mean and standard deviation? (Note: F = (1.8)(C) + 32)
• In a particular set of data,if you multiply each data value by 3 and then add 5, what effect will this have on the mean and standard deviation of the data set?