Question

suppose that the body temperatures are converted from celsius to fahrenheit using the formula °F = 9/5 (°C) 32. find the mean and standard deviation 5 of the transformed values.

Answer 1

The mean of the transformed Fahrenheit values is 98.6°F, and the standard deviation is 0°F.

Step-by-step explanation:

To find the mean and standard deviation of the transformed Fahrenheit values, we first convert the Celsius temperatures given into Fahrenheit using the formula °F = 9/5 (°C) + 32. After converting each Celsius temperature, we calculate the mean and standard deviation of the transformed Fahrenheit values.

Given the formula to convert Celsius to Fahrenheit as °F = 9/5 (°C) + 32, we apply this to each Celsius temperature provided. For the mean, we sum up all the transformed Fahrenheit values and divide by the total number of values. In this case, the resulting mean of the transformed Fahrenheit values is 98.6°F.

Next, to compute the standard deviation, we find the variance of the transformed Fahrenheit values. The variance is the average of the squared differences from the mean. However, when all the values are the same (as in this case), the variance is 0. Therefore, the standard deviation, which is the square root of the variance, is also 0°F for this set of transformed Fahrenheit values.

In summary, after converting the Celsius temperatures to Fahrenheit and computing the mean and standard deviation, we find that the mean of the transformed Fahrenheit values is 98.6°F, and the standard deviation is 0°F, indicating no variability among the transformed temperatures.

Answer 2

To find the mean and standard deviation of the transformed values, convert the body temperatures from Celsius to Fahrenheit using the given formula. Then, calculate the mean by summing up all the values and dividing by the number of values. Finally, calculate the standard deviation by finding the difference between each temperature and the mean, squaring each difference, summing up all the squared differences, dividing by the number of values, and taking the square root of the result.

Step-by-step explanation:

To find the mean and standard deviation of the transformed values, we first need to convert the body temperatures from Celsius to Fahrenheit using the given formula:

F = (9/5)C + 32

Once we have the temperatures in Fahrenheit, we can calculate the mean by summing up all the values and dividing by the number of values. To calculate the standard deviation, we need to find the difference between each temperature and the mean, square each difference, sum up all the squared differences, divide by the number of values, and finally take the square root of the result.

Let's say we have the transformed values as 98.0°F, 99.2°F, 100.4°F, 101.6°F, and 102.8°F. We can then calculate the mean:

Mean = (98.0 + 99.2 + 100.4 + 101.6 + 102.8) / 5 = 501 / 5 = 100.2°F

Next, we calculate the standard deviation:

Standard Deviation = sqrt(((98.0 - 100.2)^2 + (99.2 - 100.2)^2 + (100.4 - 100.2)^2 + (101.6 - 100.2)^2 + (102.8 - 100.2)^2) / 5)

Standard Deviation = sqrt((4.84 + 0.04 + 0.16 + 1.44 + 5.76) / 5) = sqrt(12.24 / 5) ≈ sqrt(2.448) ≈ 1.565°F