Yes it is true that the range is wide. This is to allow for variations in the production process as well as different conditions of operation like current and temperature. The typical value is usually specified too, and there is a bell shaped curve that a larger number of leds fits around this value. This allows for production spreads. It is likely the production spread is less than allowed for, because th eproduction process is usually improved over time. On average most are closer to the typical value.
For design though, you will need to consider the maximum and minimum values for a worst case situation. The voltage to use is the voltage for the current you chose.
The higher value determines the minimum supply voltage for the number of leds in series, allowing extra voltage about 20% for the ballast resistor. WIth a battery, this would be for a low battery. A regulated supply is best as that removes one of the variables.
The lower value has an effect on the ballast resistor chosen, as the current can be too high if the led string has a low voltage or the supply voltage is high.
In the end it is a compromise. Use less leds and a bigger resistor value in each series string will solve the problem, as the current is more constant. The tradeoff is more power wasted in the ballast resistor. This can be overcome by an active regulator using switchmode techniques, but that is a step too far for you I think. There is also a matter of the power dissipated by the leds and the resistors. When all bunched up they get hotter than intended, and a derating is needed (less current). The 5mm type are rated for single items in free air.
The calculator in the link seems to come up with too many leds in series. Think of the number of leds in series is for 75% of the supply for the typical Vf and supply and things will work better.. A higher supply voltage up to about 32V is more efficient, if you have a big array.