Appendix 1 APPENDIX 1. PROCEDURES FOR CONDUCTING SURVEYS AND ESTABLISHING
AVERAGE WEIGHTS FOCUS. The methodology presented can be used to determine standard average weights for passengers, checked baggage, carry-on baggage, mail, other normal averaged items and male/female ratios in lieu of using those standard average values suggested in the Advisory Circular (AC).
DETERMINATION OF STANDARD AVERAGE WEIGHT VALUES FOR PASSENGERS, BAGGAGE, AND CARGO/MAIL: It is Critical that operators determine that average weights used for passengers, baggage, and cargo/mail do not adversely affect operational safety. In lieu of using the standard average weight values contained in this AC, average weights may be generated by use of a suitable statistical analysis.
a. This appendix contains an acceptable methodology for conducting a statistical analysis and establishing suitable average weights.
b. Average weight values for adults should be based on a male/female ratio of 60/40. Use of a different ratio should be based on acceptable survey data. An acceptable methodology is shown in this appendix.
c. For practical reasons passenger weight values may be rounded to the nearest whole number in pounds, and the checked bag weight may be rounded to the nearest 0.5 pounds.
3. SAMPLING METHOD. Averages should be determined by a random sampie, 1.e., every member of the group must have a chance of selection. The process may be determined by ticket selection with random selected numbers, flight selections, airport selections with consideration given to check point or gate/flights within those airports. The process used is dependent on the diversity of the carrier's operation.
addition, the random sample must be of a conventional airline population and should consider the type of operation, the market, the frequency of flights on various routes. Significant variations in the weights should be taken into consideration.
A survey plan should cover the weighing of at least 1500 of the items being sampled or as specified in paragraph 6a(1) of this appendix, whichever is larger.
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Appendix 1
a. Passenger Weights.
(1) Adults and Children.
adults may be defined as persons of an age of 13 or more years.
They may be further classified as male or female.
differentiation of sex shall be made for children, who are defined as persons less than age 13.
(2) Survey participants should be given the assurance that all data taken will remain confidential and that under no circumstance are they obligated to participate, although participation should be encouraged. All displays of weight figures shall be arranged so that they are only visible to authorized survey people.
(3) Surveys should be conducted inside an airport location and at a site that will not inconvenience participants or other airline passengers.
(4) Carry-on baggage should be accounted for as part of the total weight of the passenger. If desired, carry-on baggage may be weighed separately and added to the passenger weight.
(5) Survey data should include, but not be limited to:
sex, adult or child categorization, survey location, weight with carry-on, weight without carry-on, date conducted, and child carried.
b. Checked Baggage.
determined by either the sum total of the actual weights of all the pieces or the actual total weights of the contents of the baggage containers they are in.
(2) As an alternative, an approved standard average bag weight, specific to the individual carrier's operation, multiplied by the total count of the number of pieces, may be used. Those average weights may be determined as specified in this document.
(3) Checked baggage averages specified in the AC may be used in lieu of determining specific averages.
(4) A form should be designed to include boarding point, destination, weight of bags or any other information pertinent to the final results. Consideration should be given to size and differences in items being sampled.
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Appendix 1 Mail.
Mail weights may be as specified in paragraph 13d of the AC.
Survey data should include boarding point, the final results. Consideration should be given to size and destination, weight of bags or - ning sampled. any other information pertinent to differences in items being sampled.
4 . SCALES. The weighing scales to be used for conducting weight surveys shall have a capacity of at least 400 pounds. All Played at weights should be displayed at a minimum interval of 1 pound and should be accurate to within ‡ ½ pound. The tolerance shall not exceed ‡ 1 pound for every 200 pounds of weight.
5. WEIGHT DATA. The recording of weight data may be done manually or automatically. All data should be retained for permanent records and as substantiation of data results.
6 . EVALUATION OF DATA. The methodology described in the following subparagraph a. should be used if the survey is being conducted to determine average weights. If the survey is being conducted to determine only male/iemale percentages, use the methodology in subparagraph i.
Calculation of Passenger Average Weight.
(1) Sample size. For calculating the required sample size it is necessary to estimate the standard deviation based on standard deviations calculated for similar populations. It is common practice to compute the precision of a sample estimate for some specified degree of reliability. A reliability of 95 percent is commonly used, 1.e., there is a 95 percent probability that the true value will fall within the specified confidence interval, around the estimated value. In order to keep the sample size at an economical level and to achieve an acceptable degree of accuracy, it is necessary to use this value for calculating the standard passenger average.
(2) Consequently, for the parameters of weight distribution three cases of mean and standard deviation have to be distinguished:
N,0 = The true value of the average passenger weight ed by weighing pare uger samand which are Par 3 Page 3
Appendix 1 M', d' = The initial estimates of the average passenger weight and standard deviation (values obtained from earlier survey samples).
*,s = The estimates for the current true values of u and o calculated from the sample.
b. Formulas. The following formulas will be necessary in determining the correct results:
(1) FORMULA - Calculation of the sample size:
n = max [1500, (1,96*0*100) *1 (e+*47)2 where:
n = No. of passengers to be weighed (sample size), e' = Allowed relative confidence range (accuracy) for the estimate of I by X,.
The allowed relative confidence range specifies the accuracy to be achieved when estimating the true mean. For example, to estimate the true mean to within ‡ 1 percent, e' will be 1 in the above formula.
1.96 = Value from the Gaussian distribution for 95 percent significance level of the resulting confidence interval.
(2) FORMULA - Calculation of the arithmetic mean:
If the sample of passengers weighed is random, the arithmetic mean of the sample, X, is an unbiased estimate of the true average weight I of the population.
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Appendix 1
(3) FORMULA - Calculation of the standard deviation:
(X;-X) 2 vn-1 where (x,-*) is the deviation of the individual value from the sample mean.
(4) FORMULA - Calculation of the accuracy of the sample mean:
The accuracy (confidence range) which can be ascribed to the sample mean, as an indicator of the true mean, is a function of the standard deviation of the sample (which is why this had to be estimated initially by ' and d'). It has to be checked after the sample has been evaluated and can be done using the following formula:
e = 1.96*5*100 (8) .
Vn*× e should not exceed:
1 percent for an adult average weight;
2 percent for an average male or female weight; or 4 percent for checked baggage and mail weights.
(5) FORMULA - Calculation of the confidence range of the sample mean:
This means that with 95 percent probability, the true average weight u lies within the interval:
X+1,96*S vn
c. Example - Adult Average Weight. The following example may be applied to any sample item. It shows the various steps required for establishing the sample size and evaluating the sample data. It is provided primarily as a guide for statistical computations. All weight figures used throughout the example are entirely fictitious.
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Appendix 1 Calculation of The Required Sample Size.
calculating the required sample size, estimates of the standard (average) passenger weight and the standard deviation are needed.
The initial estimates from an earlier survey may be used for this purpose. If such estimates are not available, a small representative sample of about 100 passengers should be weighed so that the required values can be calculated. However, the representative small sample cannot serve to be the total sample requirement. The following example assumes an 86-passenger sample.
n = 86 Step 1: Estimated average Step 2: Estimated standard passenger weight deviation (1b) (x;- x) 1 176.1 +20.5 420.2
150.1 H = x - 5.5 30.2
171.1 +16.1 259.2
164.2 + 8.6. 73.9
119.2 = LX¡ -36.4 1324.9
137.2 n -18.5 342.2
196.8 +41.2 1697.4 8 239.6 +84.0 7056.0 13385.4 86 85 139.3 = 155.616 lb. -16.3 265.6 86 166.2 +10.6 112.4 86 13,385.4 168,559.3 (X;-X) 2 g1 = vn-1 = V168,559.3 V85 = 44.531b.
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Appendix 1 Step 3: The required number ot passengers to be weighed should be such that the confidence range, e', does not exceed 1 percent.
n = max [1500, (1.96*01*100) 21 (e*47)= = max 11500, (1.96*44.53*100)21 (1*155.616)2 = max (1500, 3146) :: n = 3146 Result: At least 3,146 passengers have to be weighed to achieve the required accuracy. A plan for weighing this sample size of passengers should then be worked out.
e. Determination of Passenger Average Weight.
Step 1: After having collected the required number of passenger weight values, the average passenger weight can be calculated. For the purpose of this example, it has been assumed that 3,180 passengers were weighed. The sum of the individual weights amounts to 509, 673.0 pounds.
n = 3,180.
2x; = 509,673.0 1bS.
· = 509,673.0 3180 = 160.27 lbs.
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Appendix 1 Step 2: Calculation of the standard deviation.
• (×;-×) ≥ = 3,621,079.6 (given) s = 1 vn-1 = V3,621,079.6 V3179 = 33.75 lbs.
Step 3: Calculation of the accuracy of the sample mean.
e = 1.96*s*100 Vn*× = 1.96*33.75*100 V3180*160.27 = 0.73% Step 4: Calculation of the confidence range of the sample mean.
* * 1,96*S = Vn X ‡ 1.96*33.75 = V3180
160.27 ‡ 1.2 The result of this calculation shows that there is a 95 percent probability of the actual mean for all passengers lying within the range of 159.07 to
161.47 pounds.
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Appendix 1 I. Calculation of Male/Female Ratio. The methodology described in this section should be used only if the purpose of the survey is to determine the percentage mix of male/females.
Once determined, use the male and female weights from paragraph 10 of the AC and the percentages found in the survey to calculate the standard average adult weight.
Let :
Km = number of males in the sample k; = number of females in the sample k = Km + k; = total sample size p = percentage of males q = percentage of females p + q = 100 Sp = Sq = standard deviation of percentage *, = standard average adult weight × = standard average male weight from paragraph 10 of the AC × = standard average female weight from paragraph 10 of the AC Sm = standard deviation of male weight S& = standard deviation of female weight S= standard error of average adult weight Par 6 Page 9
Appendix 1
(1) Formulas. The following formulas should be used in determining the correct results:
(i) FORMULA - Calculation of the percentage of male and female passengers and the standard deviation.
p = Km * 100 (8) g = * 100 (%) Sp = vp*g Vk-1
(ii) FORMULA - Calculation of 95 percent confidence range for both male and female percentages.
p ‡ 1.96* Sp
(iii) FORMULA - Calculation of standard average adult weight using male and female weights from paragraph 10 of the AC.
(iv) FORMULA - Calculation of the standard deviation of the standard average adult weight.
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Appendix 1
(v) FORMULA - Calculation of the accuracy of the standard average adult weight.
e = - 1.96*57 * 100(8)
(vi) FORMULA - Calculation of the 95 percent confidence range of the standard average adult weight.
X, + 1.96 * Sxo
(vii) FORMULA - Calculation of the sample size.
k = max 1500,. (×т-Х¿) ?*р*а g'*s} e*.
1.96 ) Note: Data from the surveys yielding the averages in paragraph 10a of the AC may be used to derive the sample size needed for update surveys. These values apply:
nm = 1039; n = 640; × = 195; X = 155; p =.619; g = .381;
* = 180; Sm = 35.1 and S; = 34.8.
Thus, for male/female averages, e = .02, and k = max 1500, (40%*,619*,381) (-02*280)2 - + (-•381) * (34.8) 3|7 = тах (143, 1500) : k = 1500 This sample size can be used until the average weights in the AC are updated with later survey data.
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Appendix 1
g. Example - Male/Female Average. The following example may be applied to any sample. It shows the various steps required for evaluating the sample data. It is provided primarily as a guide for statistical computations. All weight figures used throughout the example are entirely fictitious.
Given: Sample of 1,500 passengers, 910 male and 590 female.
Step 1. Calculating the percentage of males and females.
p = Km * 100 910 * 100 1500 = 60.7% ₫ = 100.0 - 60.7 = 39.38.
Step 2. Calculation of the standard deviation. Note that the standard deviations for the percentage of men and women are equal.
Sp = vp*g vn-1 = V60.7*39.3 V1499 = 1.26% Page 12 Par 6