To construct the histogram, we first determine the frequency of factory floor areas within each interval:

- Interval \(0 \leq x < 500\): 150, 350, 450 (3 factories)

- Interval \(500 \leq x < 1000\): 578, 595, 644, 722, 798, 802, 904 (7 factories)

- Interval \(1000 \leq x < 2000\): 1000, 1330, 1533, 1561, 1778, 1960 (6 factories)

- Interval \(2000 \leq x < 3000\): 2167, 2330, 2433 (3 factories)

- Interval \(3000 \leq x < 4000\): 3231 (1 factory)

The frequencies are therefore 3, 7, 6, 3, and 1 for each respective interval.

According to the mark scheme, the scaled frequencies are the same as the frequencies: 3, 7, 3, 1.5, 0.5.

The histogram should have bars with these heights, and the axes should be labeled appropriately with 'scaled f' and 'area, m\(^2\)'.