# § 83.05 – How should I determine the APTL from my sample?

(a)    You must determine the sample APTL for a given sample as the ratio of sample total PMT over sample total UPT for the following cases:

(1)   for the entire sample,

(2)   by type of service days, or

(3)   by service group if applicable.

(b)   You must not determine the sample APTL as the average of the APTL across individual service units in the sample.

(c)    To determine the weighted sample APTL for an entire sample as required by question §83.03(c)(3), you should follow these steps:

(1)   Determine each group’s size in the number of service units actual operated.

(2)   Compute each group’s share of the number of service units actually operated.  These shares must sum to 1.

(3)   Determine each group’s sample size in the number of service units in the sample.

(4)   Determine each group’s sample total UPT.

(5)   Determine each group’s sample total PMT.

(6)   Compute each group’s sample average for UPT.

(7)   Compute each group’s sample average for PMT.

(8)   Sum the product of each group’s share of the number of service units actually operated and its sample average UPT.

(9)   Sum the product of each group’s share of the number of service units actually operated and its sample average PMT.

(10)           Compute the ratio of the result from (9) to the result from (8).  This ratio gives the weighted sample APTL.

(11)           Table 83.01 shows these steps with an example.

Table 83.01.  Example of Estimating Weighted Sample APTL

 Step Description Service Groups Short Routes Medium Routes Long Routes 1 Group size in service units 109,685 331,033 35,325 2 Group size in shares 0.2304 0.6954 0.0742 3 Sample size 116 386 47 4 Sample total UPT 1,157 8,181 1,592 5 Sample total PMT 3,989 42,966 7,003 6 Sample average UPT 10.0 21.2 33.9 7 Sample average PMT 34.4 111.3 149.0 8 Weighted sample average UPT 19.55 9 Weighted sample average PMT 96.38 10 Weighted sample APTL 4.93