Here are the summary statistics for 31 daily high temperatures of a location in degrees Fahrenheit. What are the corresponding numbers in degrees Celcius?
| Mean | 86.6 | oF |
| Median | 87.3 | oF |
| Standard Deviation | 5.2 | oF |
| Variance | 27.04 | oF |
Central tendency and variability during transformations
A few exercises before try and estimate the answer.
A few exercises before try and estimate the answer. Consider three numbers, 5,6,7. The mean, median, standard deviation and variance o the collection are 6, 6, 1 and 1.
Now add 3 to each and find the summary statistics:
The new set is 8, 9, and 10 and the summary is 9, 9, 1, 1. The mean and median of the new set are just 3 more than the original, and the variance and the standard deviations are unchanged.
Multiply each by 4 and the summary statistics:
The new set is 20, 24, and 28 and the summary is 24, 24, 4, 16. The mean and median of the new set a4 times the original, and the variance is 4 times and the standard deviation is 42 times.
Transformation of oF to oC
The relationship (which is a linear transformation is)
C = (5/9) x (F – 32)
C = -(160/9) + (5/9) F
Applying what we learned earlier,
Mean in oC = -(160/9) + (5/9) x 86.6 = 30.3
Median in oC = -(160/9) + (5/9) x 87.3 = 30.7
Standard deviation in oC = (5/9) x 5.2 = 2.89
Variance in oC = (5/9)2 x 5.22 = 8.35
Linear Transformations: jbstatistics
