6) Suppose you had the following body temperature readings, all in °F: (Don't forget to answer the questions in parts (d) and (e)). 96.21 97.65 97.39 97.97 97.28 99.43 a) calculate the mean, variance and standard deviation. b) now convert these readings to °C (us biologists like the metric system, after all). To convert, remember that °C = °F/1.8 - 32/1.8. For example, to convert the first reading you would do: 96.21/1.8 - 32/1.8 = 53.43 - 17.78 = 35.67. c) now calculate the mean, variance and standard deviation of the converted data. d) take the mean you calculated in (a) and convert this to Celsius using the same formula you used in (b). Are you surprised by the results? Why or why not? e) take the standard deviation from (a) and divide it by 1.8. Can you explain the results? Why didn't you have to subtract 32/1.8? Watch your math in this step!
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
6) Suppose you had the following body temperature readings, all in °F: (Don't forget to answer the questions in parts (d) and (e)).
96.21 97.65 97.39 97.97 97.28 99.43
a) calculate the mean, variance and standard deviation.
b) now convert these readings to °C (us biologists like the metric system, after all). To convert, remember that °C = °F/1.8 - 32/1.8. For example, to convert the first reading you would do:
96.21/1.8 - 32/1.8 = 53.43 - 17.78 = 35.67.
c) now calculate the mean, variance and standard deviation of the converted data.
d) take the mean you calculated in (a) and convert this to Celsius using the same formula you used in (b). Are you surprised by the results? Why or why not?
e) take the standard deviation from (a) and divide it by 1.8. Can you explain the results? Why didn't you have to subtract 32/1.8? Watch your math in this step!
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