 ### Double carriage Millionaire vs. TIM-Unitas

This is a little test of the same sum of products on a manual TIM-Unitas machine and on an electric double carriage Millionnaire, which is a direct multiplication machine, and should thus be much faster. The data come out of an exercise book on machine calculation of statistics.

These are the numbers:

56.09 x 498

68.87 x 537

49.30 x 465

53.09 x 500

74.78 x 698

------------

166581.95

I've used the TIM a little inappropriately, because it does not have tens' carry in the counter register, so that means when using abbreviated multiplication as I have done in this example, the multipliers don't show cleanly in the multiplier register, and checking the calculation is difficult. This is another point in favour of the Millionnaire. Calculations become progressively faster on the Millionaire as the factors become longer - in the TIM it is a real must to place the four-digit number on the keyboard, and if a double check has to be done by doing the calculation again by reversing the factors of the products, this is a real pain. On the Millionaire, it makes no real difference.

The only thing which is a little odd and disconcerting at first on the Millionaire is that it starts calculating on the left-hand side of the register, and then down by decades when multiplying. For me the logical order would be to start with the units, then go up to the tens, hundreds, etc., in order to use up all the space on the right of the register, but that is not how a Millionaire works. This means that placing the decimal points for me is rather difficult due to lack of routine, and the confusing shifts of the carriage that the machine makes. It is important to remember that the Millionaire will first multiply by the tens, then shift the carriage and do the units, so in the end your result is one place further to the right than you would originally expect. I've never managed to make a correction for a miscalulation correctly so far.

For this video I've adopted the same strategy (multiplying from high to low) for the TIM-Unitas as for the Millionaire - quite possible, because the number of digits and the position of the decimal point is the same in all of the lines. It would be much more difficult if it weren't!

Now, here's the video:

If the keying of the numbers seems a little hesitant, it is because I have to refer to the small print in the statistics book.

Results:

• TIM-Unitas: 1m 35s
• Millionaire: 1m 8s
• electronic calculator: 41s

### Simple statistics on the double carriage Millionaire

The next video shows how the double carriage Millionaire can be used to good effect for some more statistics calculations. I found a data set with the weights of 9 baseball center players. In kg, they weigh 95.3; 115.7; 108.9; 106.6; 106.3; 113.4; 114.3; 111.9 and 131.5.

The video starts with the sum of these nine numbers (1003.9). Subsequently, we divide by 9, to get the average (111.54444). Average known, we can now subtract it from each of the weights, and square the result. This gets added to the top carriage, that then gets disconnected, so all it does is accumulate the squared differences, while the rest of the calculations happens in the bottom register.

At the end of the story, we then have the sum of squared differences (749.482), and divide it by the number of samples minus 1 (which yields the variance - 93.6853), and finally, we take the square root of this number to provide the sample standard deviation (9.679116).

All of this took 20 minutes, and it will be progressively longer if the number of samples increases. Originally, I started with a set of 30 samples, but I quit when I was halfway through. Calculating statistics without a computer was not a fun job - and in addition, ear protection was not an excessive luxury!

Here's the video: