Don’t round off numbers before mathematical operation

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

21 August 2022

A day after the declaration of the presidential election results, the country was treated to some mathematical entertainment when a member of the Independent Electoral and Boundaries Commission (IEBC) announced at a press conference that the data announce by IEBC Chairman Wafula Chebukati was inconsistent. In her own words: “a mathematical absurdity that defies logic”. She pointed out that to total percentages came to 100.01 per cent and claimed that the extra 0.01pc represented about 140,000 votes out of the 14 million that were cast.

Let’s put aside the obvious arithmetic error and tackle a more pertinent question: can percentages ever add up to more than (or even less than)100? The answer is no and yes!

The IEBC Chairman announced that Odinga got 48.85 per cent of the valid votes; Ruto 50.49; Waihiga 0.23 and Wajackoyah 0.44. The total is 100.01 per cent. If we round to the nearest whole number, we get 49, 50, 0 and 0 respectively; and the sum is now 99 per cent.

This is nothing strange. When working with numbers, it is important that any operation (for example, addition) must be done before rounding. What we are doing here is the reverse (rounding before adding) and for that, the accuracy is lost hence the answer may not be exactly correct.

Some people were quick to round the numbers to ten decimal places and demonstrate that the total comes to 100. However, when expressed to 13 decimals, they don’t add up to 100! When rounded to three decimal places, the sum comes to 100.000. Try it for yourself…

Why did IEBC choose to round the percentage to two decimal places? I can’t see any good reason. If I was consulted, I would have use just one decimal place. Thus: Odinga – 48.8; Ruto – 50.5; Wajackoya – 0.2 and Waihiga – 0.4. Totalling 99.9.

Before some one comes to correct me on Odinga’s number; let me point out that the 48.85 read out by Chebukati was rounded from 48.849; hence it becomes 48.8 when expressed to one decimal place.

Finally, is it necessary to work out the percentage? The answer is no. The constitution does not require such calculation. It simply says that the winner must get “more than half of the votes cast”. So, IEBC should have proceeded as follows:

Total valid votes cast = 14,213,137; Half of this is 7,106,568.5; Ruto got 7,176,141 which is more than the half of 14,213,137. Case closed!