Why the Bureau of Statistics change inflation formula
By MUNGAI KIHANYA
The Sunday Nation
Nairobi,
15 November 2009
The inflation rate is now in the single-digit level standing at 6.6 per
cent in last month. This is a big drop from the September value of 17.9
per cent. The reason for the difference, however, is not that the
economy has had a sudden boost: It is because the Kenya National Bureau
of Statistics (KNBS) has changed the formula used in calculating the
figures.
The Bureau of Statistics has moved from Arithmetic to Geometric mean
and, as a result, the inflation figures have changed. Now why it was
necessary to change the method of calculation?
The arithmetic mean is the average that most people know about. It is
obtained by adding up the values at hand and then dividing the result by
the number of figures. For example, if five shops quote the price of a
certain item as sh23, sh24, sh26, sh27 and sh28 the arithmetic mean is
simply the sum [sh128] divided by five. The answer is sh25.60.
Geometric mean on the other hand, is obtained by multiplying all the
figures and then finding the N-th root of the result, where N is the
number of figures. Thus if there are two figures, you get the square
root; if there are three, you calculate the cube root, and so on.
In the previous example, the geometric mean would be the fifth-root of
the product of the prices [10,850,112]. The result is sh25.53 – seven
cents lower than the arithmetic mean.
In this example, however, the arithmetic mean is the “better” average
since the values under consideration are not related to one another.
Each shopkeeper sets their price depending on the specific circumstances
he/she faces.
Geometric mean on the other hand is more appropriate when we are working
out the average of percentages. For example; suppose the price of an
item at a particular shop [note; this is ONE shop, not many shops as in
the previous example] starts from sh23 in one week and then changes
weekly to sh24, sh26, sh27 and sh28 in the subsequent weeks. What is the
average percentage change in prices during the period?
The arithmetic mean is obtained as follows: The first change is 4.35 per
cent [from sh23 to sh24], the next is 8.33 [sh24 to sh26], followed by
3.85 [sh26 to sh27], and finally 3.70 per cent [sh27 to sh28],
respectively. The sum of these percentages is 20.23 per cent, thus their
arithmetic mean is 5.06 per cent [20.23 divided by 4].
But is this a “good” average? To find out, we start from sh23 and add
5.025 percent four times, consecutively and see what we get. The answer
is sh28.02. This is slightly higher than the final price of sh28.
In order to find the geometric mean, we must first convert the
percentages into factors; that is, 1.0435, 1.0833, 1.0385 and 1.0370
instead of 4.35, 8.33, 3.85 and 3.70 per cent respectively.
The geometric mean of these factors is 1.0504 (or 5.04 per cent). If we
repeat the test and increase the price by 5.04 per cent four times
consecutively starting from sh23, we shall get exactly sh28. Therefore,
this is a better way of calculating the average percentage increment.
In this example, the arithmetic average “inflation rate” is 5.06 per
cent while the geometric one is slightly lower at 5.04 per cent.
However, if repeated over a long period of time, the difference between
the two can be extremely large, as happened in the case of
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