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Federal Register / Vol. 86, No. 29 / Tuesday, February 16, 2021 / Rules and Regulations
the indexing regime. In proposing to average the weighted mean with the median and unweighted mean to derive the composite central tendency, Dr.
Kahn explained that each of these measures captured a significant aspect of the composite results from an industry perspective. 76 The Commission credited Dr. Kahns testimony and adopted this approach to calculating the composite central tendency in that proceeding and in all subsequent five-year reviews. As discussed below, we find that Liquids Shippers arguments do not provide an adequate basis for departing from this consistent practice.
37. Second, we reject as unpersuasive Liquids Shippers claim that the Commission should replace the weighted mean merely because it provides greater weight to larger pipelines like Colonial and Enbridge.77
The index strives to track cost changes
on an industry-wide basis among pipelines of all sizes. To this end, the Kahn Methodology strikes a balance between large and small pipelines by determining the central tendency of the cost data using two measures that do not take pipeline size into account the median and the mean together with the weighted mean, which weights each pipelines cost change by its transported volumes. Including the weighted mean in this analysis ensures that the costchange calculation takes sufficient account of pipeline size so that minor pipelines do not skew the result.78
Thus, the fact that the weighted mean may accord additional weight to larger pipelines in this data set is fully consistent with its role in the index calculation. Removing it from the analysis as Liquids Shippers propose would upset the balance between large and small pipelines that the Kahn Methodology achieves. For this reason,
we likewise reject Liquids Shippers alternative proposal to reduce the weighting of the weighted mean in the calculation from 33.3% to 20% or 10%.
38. Third, Ms. Crowes calculation of the weighted median is methodologically flawed. AOPLs witness Dr. Shehadeh testifies that the established statistically appropriate method for calculating the weighted median, as applied to pipeline cost changes, is to identify the cost change in the data set for which the same share of barrel-miles rather than the same number of pipelines is accounted for by the pipelines below and above the selected median.79 Shehadeh Reply Decl. at 11 n.17 citing Thomas H.
Cormen, Introduction to Algorithms 194
2009; 6 F.Y. Edgeworth, On Observations Relating to Several Quantities 27985 1887 The weighted median may be defined as follows:

This value is appropriately derived by ordering the pipelines by cost-change percentage, computing each pipelines share of total barrel-miles, and measuring the cumulative share of total barrel-miles represented as each pipeline is included in the sample.80
The pipeline whose share of total barrelmiles causes the cumulative share to reach 50% represents the data sets weighted median.81
39. Ms. Crowe, however, performed a different calculation by identifying the
median weighted barrel-mile costchange percentage and dividing that figure by the average of those pipelines 2014 barrel-miles.82 This calculation departs from the proper method of calculating the weighted median discussed above. Rather than identify the pipeline that causes the cumulative share of total-barrel miles represented in the sample to reach 50%, Ms. Crowe derives the median value of the weighted cost-change percentages for 2019 without regard to the barrel-miles
represented below and above that cost change.83 Unlike the Commissions calculation of the standard median and Dr. Shehadehs calculation of the weighted median, Ms. Crowe does not order pipelines by cost changes, and instead orders them by cost changes times barrel-miles.84 Thus, the median of Ms. Crowes data sample does not capture the central tendency of industry-wide cost changes, as evidenced by the significant and multidirectional fluctuations above and
76 Testimony of Dr. Alfred E. Kahn, Docket No.
RM9311000, at 9 filed Aug. 12, 1993.
77 The Commission has previously recognized that large pipelines like Colonial can exert significant influence upon the weighted mean. 2015
Index Review, 153 FERC 61,312 at P 24 n.49
explaining that because Colonial is a large pipeline, it heavily influences the weighted average in the Kahn Methodology.
78 AOPL II, 281 F.3d at 241. Although Order No.
561A recognized that the median is often the preferred statistical measure of central tendency where the distribution is highly skewed, the Commission made this observation in affirming the use of statistical data trimming to derive a median sample of the overall data set rather than in the context of using the median to determine the data sets central tendency. See Order No. 561A, FERC
Stats. & Regs. 31,000 at 31,09697. In that proceeding and in each subsequent index review, the Commission has consistently calculated the composite measure of central tendency by averaging the median, mean, and weighted mean.

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79 Shehadeh
Reply Decl. at 11.
example, consider a set of numbers 3, 4, 6, 10, where each number is weighted 1, 2, 3, and 5, respectively. In this scenario, the weighted median of the data set would equal 6, because including 6
in the set increases the cumulative weighting to 50%. 1+2+3/1+2+3+5 = 6/11 = 54.55%. By contrast, the standard median would be 5, which equals the average of the second and third numbers of the set.
81 Dr. Shehadeh correctly performs this calculation using Liquids Shippers data set and derives a weighted median cost change of 0.68%, as reported by Enbridge. Shehadeh Reply Decl., App. B, Ex. 1.
82 Shehadeh Reply Decl. at 13; see also Crowe Initial Aff., App. 6 at Cost Changes Tab. Although Ms. Crowes testimony on this issue was unclear, our understanding of her calculation is as follows.
First, she identified the pipelines with percentage cost changes in the middle 50%. Second, she multiplied each pipelines percentage cost change by its barrel-miles. Third, she arranged the 80 For
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pipelines based upon these results from smallest to largest. Fourth, she determined the median of this data sample. Because Ms. Crowes sample consists of an even number of pipelines, the median lies at the midpoint between two pipelines, Hilcorp Pipeline Company, LLC, and BOE Pipeline, LLC.
Finally, she divided the median percentage cost change by those pipelines 2014 barrel-miles, which produces a final result of 0.57%. See Crowe Initial Aff., App. 3, at Cost Changes Tab; Shehadeh Reply Decl. at 10, Figure 1 and App. B, at Figure 1Chart Backup Tab.
83 In essence, Ms. Crowe attempts to calculate the weighted median by using a modified version of the formula the Commission uses to compute the weighted mean.
84 See Crowe Initial Aff., App. 3 at Cost Changes Tab. Under this approach, it is unclear whether the median pipeline of a given sample reported a relatively high cost changes and low barrel-miles or b relatively low cost changes and high barrelmiles.

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