why the average of the two 95% confidence interval limits for lower and upper speeds not equal to average speed based on average running time ?

Question

for example : Given the normal distribution of running times, the
mean running time for the section (3mi) is 196 seconds, and 95% of
all running times would fall within 1.96(15) = 29.4 seconds of
this value. Thus the 95% interval for travel times would be
between 196 - 29.4 = 166.6 seconds and 196 + 29.4 = 225.4
seconds. The speeds corresponding to these running times
(including the average) are:
S 1 = (3mi/225.4s)*(3600s/h) = 47.9 mi/hr
S av =(3mi/196s)*(3600s/h) = 55.1 mi/hr
S 2 = (3mi/166.6s)*(3600s/h) = 64.8 mi/hr

S1 + S2 not equal to =55.1 why?

Answer 1

Even though there is a linear relationship between the three running times when you divide a constant (e.g. 3) by each your three resulting quotients do not have to be linear.

 

Take the 3 numbers 2,3,4; 2 and 4 have an average of 3 but if you divide 3 by 2,3,4 you get 1.5,1,.75 which is not linear.

 

Do you understand?