11. The effect of transformations of scale on the mean and standard deviation Aa

Question

11. The effect of transformations of scale on the mean and standard deviation Aa Aa You just completed a small research project for your psychology class concerning the effects of an event that happened five years ago on women's opinions and actions today. The mean age of participants in your study is 25.4 years with a standard deviation of 3.6 years. As you write up your results, you realize that what matters is the ages of the participants five years ago when the event happened, not their ages now. You decide to subtract 5 from each of your participants' ages. After you subtract 5 years, the mean age in your sample is years. The new standard deviation of the ages in your sample is years One of the variables you collected was the study participants' heights in centimeters. The mean height of participants in your study is 168.1 centimeters with a standard deviation of 8.4 centimeters. Your professor, however, requested that you report this value in inches. To convert from centimeters to inches, you multiply by 0.394. After you multiply the heights of your participants by 0.394, the mean height in your sample is deviation of the heights in your sample is inches. The new standard inches.

Explanation / Answer

a) The mean will be reduced by 5 but there would be no change in the standard deviation because change of origins doesn't affect the value of standard deviation. Hence,

The answers will be:

New mean = 20.4

Standard deviation = 3.6

b) In this case, both the quantities will be multiplied by 0.394. Hence,

New mean = 66.2314 inches

New standard deviation = 3.3096 inches

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