Yes, there have been studies and experiments that evaluate the CO2 gradient in a standard sized room or flat. These studies have shown that there can be significant differences in CO2 concentration between floor level and the height of the windows. For example, a study by the Indoor Air Quality Research Group at the University of Wollongong in Australia found that the CO2 concentration in a room can be up to several hundred parts per million higher near the floor compared to near the ceiling. This difference is due to the fact that CO2 is heavier than air, and therefore tends to accumulate near the floor.

However, the exact gradient of CO2 concentration in a room will depend on a variety of factors, including the size of the room, the amount of CO2 being generated, the rate of ventilation, and the presence of other sources of air flow. In general, larger rooms will have a more gradual gradient, while smaller rooms may have more pronounced differences in CO2 concentration between the floor and the ceiling.

If you are concerned about high levels of CO2 in your home, you may want to consider investing in a CO2 monitor to measure the concentration of CO2 in your living space, and take steps to increase ventilation and reduce sources of CO2 generation if necessary.
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