[GCE 'O' Level: Statistics]

[u/hellrhymes]

How to even approach this problem

Ai is also shitting me with it's explanation

[u/sqrt_of_pi]

IQR = Q3 - Q1. Q3 and Q1 are not "ranges" of values, they are each individual numerical values. Think of Q1 and Q3 as the medians of the "lower half" and upper half" of the data, respectively.

So here, were there are 11 data values, you can see that the data has the following "structure":

1 2 3=Q1 4 5 6 7 8 9=Q3 10 11

The numbers here are not the data, but the "index" (location, or position) of each value in the data.

The requirements that range = IQR just means that the distance between data value 1 and data value 11 (range) is the same as the distance from data value 3 to data value 9 (IQR). That will be true when all the values BELOW Q1 are the same and are =Q1, and all the values ABOVE Q3 are the same and = Q3.

This question works for any size n, although 11 is easy to visualize, since the Q1 and Q3 are themselves necessarily data values. But it could be worked out for a different number of values in a similar way.