A company employs 2410 people whose annual salaries are summarised as follows:

<10 10-20 20-30 30-40 40-50 50-60 60-80 80-100 >100 (i.e. 100-140)

16 31 502 642 875 283 45 12 4

First row: salary (in $1000)

Second row: number of staff

Find the upper and lower quartile.

This should be fairly straightforward, I drew a quick cumulative frequency graph, came up with 603rd term for the lower quartile, 1808th term for the upper quartile; this is correct right?

Anyway I got lower quartile around $30 130, upper quartile $47 700

But the answers turned out to be $15 420 and $23 520 respectively, i.e. almost exactly half of each of the values I found.

But how are those answers even possible, with the largest frequencies between 30 and 60? it just doesn't seem logical.