The density of water at 4°C is supposed to be 1000 kg m^–3. Is it same at the sea level and at a high altitude?

The density of water is related to temperature. At the temperature of 4°C the density of water is the highest. Atmospheric pressure is inversely proportional to altitude. So, when altitude increases, the atmospheric pressure decreases. According to the equation P=hρg, where ρ=density of fluid and P is the pressure of fluid, pressure depends on density. Therefore at 4°C, as the pressure is less, the water density at high altitude will be lower compared to sea level density.