I just started looking at GMAT questions to practice more of the “data” questions and came across this chart question:
Which of the following statements can be inferred from the data above?
I. The Klein family’s annual income more than doubled from 1985 to 1995.
II. The Klein family’s annual income increased by a greater amount from 1985 to 1990 than from 1990 to 1995.
III. The Klein family’s average (arithmetic mean) annual income for the period shown was greater than $40,000.
A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III
I knew I. is correct because the income in 1985 was around 25K and in 1995 it was around 64K so the income more than doubled from 1985 to 1995.
II. is wrong because the % increase from 1985 to 1990 is 56% while the % increase from 1990 to 1995 is around 65%
Now, for the III. question I knew there must be some shortcut instead of actually calculating the average so the way I approached it was that we have 7 data points that are below 40K and 4 data points that are above 40K so the avg must be below 40K (cause 7>4 so 7 data points are pulling the avg towards that side.)
I ended up choosing A but turns out the correct answer is C. Could someone explain why my approach to the III. part gave me the incorrect answer? Thanks in advance!
Yes, there are 7 points below 40k and 4 points above that.
But, you have to consider the values too, not just the number of points.
Let’s assume that 40k is the threshold line. The points below the threshold line are negative and above that threshold line are positive.
Then you can estimate the distance from that threshold line.
The distance of all the 7 points below the threshold line = |-15k -14k -14k -5k -2k -2k| = |-52k| = 52k
The distance of all the 4 points above the threshold line =|23k + 23k + 23k + 17k| = |+85k| = 85k
And 85 > 52
Thus, It’s obvious that the points above 40k are dominating the average value (even though the number of the values is 4). In other words, the average tends to skew towards the side greater than 40k.
So, The Klein family’s average (arithmetic mean) annual income for the period shown was greater than $40,000. And this statement is true.
As we see from this screeshot below,
After the cancellation of 3 data points I circled above 40k and 3 data points I circled below 40k, we still left approximately 60K more (15-9) above 4k line. Then we could safely guarantee the sum of the remaining 4 data points(below the 40k line) is smaller than 6, which is like 2 approximately from observation, cancel again, we left like 40k+30k. So in total, above the 40,000
