The effect of transformation of scale on the mean standard deviation You just co

Question

The effect of transformation of scale on the mean standard deviation

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 action today. The mean age of participants in your of participant in your study is 42.5 years with a standard deviation of 6.1 years . As you write up your result, you realized 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’ height in inches. The mean height of participants in your study is 64.3 inches with a standard deviation of 3.9 inches. Your professor, however, requested that you report this value in centimeters. To convert from inches to centimeters you multiply by 2.54. After you multiply the heights of your participants by 2.54, the mean height in your sample in ___________centimeter. The new standard deviation of the heights in your sample is______________ centimeters

Explanation / Answer

The mean age of perticipants is 42.5 years and the standard deviation is 6.1 years.

Now we subtract 5 years from each of the perticipants age.

The new mean age of the perticipants is 42.5-5=37.5 years.

The variance does not depend on the change of scale, therefore the standard deviation remains the same, i.e. 6.1 years.

The mean height of perticipants is 64.3 inches with standard deviation 3.9 inches.

To convert from inches to cm, we multiply the observations by 2.54. the mean height become 64.3*2.54=163.322 cm

The standard deviation become 3.9*2.54=9.906 cm.

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