The question asked:
Consider a dataset D.
Quantity A: The average of the values at the 49th and 51st percentiles of D
Quantity B: The Q2 value of D
I didn’t quite understand Greg’s explanation for this, but I arrived at the same conclusion with different reasons, and I wonder if my reasons are valid.
Quantity\:A = Quantity\:B when all the values on dataset D is the same.
Quantity\:A > Quantity\:B when the value at the 51st percentile is a lot larger than the value at the 49th or Q2 (or the median). For example, let:
the\:value\:at\:49th\:percentile = 49
the\:value\:at\:50th\:percentile = 50
the\:value\:at\:51st\:percentile = 1,000
Then, the\:average\:of\:the\:values\:at\:the\:49th\:and\:51st\:percentiles = (49+1000)/2=524.5. This means that:
Quantity\:A = 524.5
Quantity\:B = 50
Hence, Quantity\:A > Quantity\:B
Is my reasoning correct here?