Appendix C 



How to Use Table C-I to Approximate 

 Coefficients of Variation 



Find the line on table C-I which is nearest to the number of 

 establishments in the estimate for which the coefficient of variation is 

 desired. For any estimate except one involving a breakdown by type of 

 establishment obtain the approximate coefficient of variation from the 

 first column. If the estimate is for a particular type of establishment, 

 use the second or third column depending on the type of establishment, 



As an example of the use of the table consider the estimates of 

 the number of public eating places obtaining their supplies from whole- 

 salers (table 55). In the Northeast region, an estimated 145^200 establish- 

 ments received their supplies from wholesalers. Table C-I indicates the 

 approximate coefficient of variation of this estimate is 8 percent. An 

 estimated 81,300 restaurants received their supplies from wholesalers, 

 Reading from the second column of this table, we would place the co- 

 efficient of variation of this estimate between h percent and 6 percent. 



Table C-I can also be used to compute the approxijiiate co- 

 efficients of vai'iation of percentages of establishments. In this case, 

 to find the approximate coefficient of variation in table C-I, first 

 divide the estimate in terras of niunber of establishments by one minus the 

 estimated proportion. For example, consider again establishments in the 

 Northeast obtaining supplies from wholesalers, but this time as a pro- 

 portion of all establishments serving fish or shellfish in the Northeast, 

 This proportion is 15,200 divided by 68,000 or 66 percent. U5,200 divided 

 by 1 minus ,66 is 133,000 and the coefficient of variation applying to 

 this number according to table C-I is between h percent and 5 percent. 

 It is pointed out that the result is a coefficient of variation, not a 

 standard deviation. The standard deviation (in percentage points) can 

 be obtained by multiplying the coefficient of variation by the percentage 

 (in the example given, the standard deviation is 66 percent times k per- 

 cent or about 3 percent) , 



Tables C-II to C-VI 



In order to approximate the sampling variability (coefficient 

 of variation) of aggregates other than the number or percentage of es- 

 tablishments, table C-II should be used. 



For such quantitative estimates, e.g., number of pounds of 

 frozen fish and frozen shellfish in cold storage, the approximate 

 sampling error is found by first obtaining from table C-IV the number 

 of establishments furnishing a non-zero report on the items. Then find 

 the line in table C-II having the number of establishments nearest this 

 number and obtain the coefficient of variation from the appropriate 

 colxunn. The coefficient of variation for the number of main dish meals 

 and sandwiches served, and quantity, value and price per pound of 

 certain species of fish and shellfish bought may be found in a similar 

 manner (tables C-III, C-V, and C-VI). 



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