292 



REPORT — li 



rule is to find that one of the entries in column 2 which has as many 

 observations above as below it : that is the ninth in the order of magni- 

 tude ; which proves to be 94. For the weighted or corrected Median we 

 still seek the entry in column 2, which has as many observations above it 

 as below it ; but we proceed as if the observation 71 had been made, not 

 once, but 19-5 times ; the observation 72 made 12-8 times, and so on. 

 There being in all nearly 177 such constructive observations, the Median is 

 the 89th, that is 94. Or in other words we have to find in the fourth column 

 that figure which is such that the sum of all above [or below] it iviih the 

 figure itself should be greater than half the sum of the entire column, 

 but loithout that figure should be less than half the entire sum. The 

 figure thus defined proves to be 6' 2. For the sum of the entries above 

 that figure is 82'3, and the half sum of the column is 88'25. Now 823 

 is less than 88'2.5, while 82'3 + 6'2 is greater than 8H'25. The entry in 

 the second column which corresponds to the figure thus determined, 

 viz., 94 (corresponding to 6'2), is the required Weighted Median} The 

 weighted Arithmetic Mean as calculated by Mr. Palgrave is 90.' By a 

 similar operatiou performed on the export statistics for the year 1880, 

 given by Mr. Giffen in his report of the year 1881, it is found that the 

 Weighted Median (for the decline of price compared with 1861) is — 7"8. 

 Mr. Gilfen's result, the corresponding Weighted Arithmetic Mean, is 

 -5-83. • 



The operation is much simplified by noticing that it is sufficient to 

 arrange the percentages in the order of magnitude in the neighbourhood 



Mean ; which, as rudeh' estimated from the disijersion of the entries in the first 

 column, is as likely as not to be as much as 2 or 3, and may not improbably be 

 4 or even 6. The difference between the systems is apt to he less, when the number 

 of independent entries is greater. In the example cited from Mr. Giffen's statistics 

 (where the number of entries is 58) the two systems of weiglits give identical 

 results. 



' As to the import of these discrepancies see the preceding note. 



