Quantitative Reasoning

Quantitative Reasoning

consider the following example of an index:

Let’s say these are the amounts that you saved over the past year. You saved cash and you saved Frequent Flyer Miles, which you converted to cash saved. Then you calculated the total.

Cash Saved Freq Flyer Miles Accumulated Cash Saved if Miles Used for Business ($20/1,000 Miles) Total
Jan $57 5,000 $100 $157
Feb $101 10,000 $200 $301
Mar $113 2,500 $50 $163
Apr $100 12,500 $250 $350
May $90 1,000 $20 $110
June $115 2,500 $50 $165
July $100 12,400 $248 $348
Aug $88 6,000 $120 $208
Sep $127 0 0 $127
Oct $135 1,000 $20 $155
Nov $109 5,500 $110 $219
Dec $20 500 $10 $30

An index serves to permit a quick comparison of the value of subsequent numbers, calculated from a “base number.”

If we use Jan as the base number, Jan becomes worth 100; all subsequent numbers are based on Jan. So if Jan = 157, what would Feb’s index be?

It’s like asking the following: If something cost $157 and were marked up to $301, what percentage mark-up does $301 represent? (We take the 92% mark-up and add 100 to get the index) For March: If something cost $157 and were marked up to $163, what percentage mark up is that? (We take the 4% mark-up and add 100 to get the index)

Cash Saved Freq Flyer Miles Accumulated Cash Saved if Miles Used for Business ($20/1,000 Miles) Total Index
Jan $57 5,000 $100 $157 100
Feb $101 10,000 $200 $301 192
Mar $113 2,500 $50 $163 104
Apr $100 12,500 $250 $350 223
May $90 1,000 $20 $110 70
June $115 2,500 $50 $165 105
July $100 12,400 $248 $348 222
Aug $88 6,000 $120 $208 132
Sep $127 0 0 0 0
Oct $135 1,000 $20 $155 99
Nov $109 5,500 $110 $219 139
Dec $20 500 $10 $30 19

 
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