Terms related to probability and statistics

Statistics
Numerical facts or data collected and classified (courtesy of the Shorter Oxford English Dictionary).

Probability
The amount of antecedent likelihood of a particular event, as measured by the relative frequency of occurrence of events of the same kind in the whole course of experience (courtesy of the Shorter Oxford English Dictionary).

Normal
The average or mean of the observed quantities (courtesy of the Shorter Oxford English Dictionary).

Mean
The result of adding up all values and dividing the total by the number of values. The average amount. It belongs to the general class of weight statistics. See the example given below for the difference between mean and median.

Median
It is the value above and below which lie half the scores in a distribution. It is the half way mark. It belongs to the general class of point statistics. See the example given below for the difference between mean and median.

The difference between the mean and median is revealed in the following examples:

(a) 1, 2, 9 ....... median 2.0 .... mean 4.0
(b) 1, 8, 9 ....... median 8.0 .... mean 6.0
(c) 1, 2, 8, 9 ... median 5.0 .... mean 5.0
(d) 1, 2, 3, 9 ... median 2.5 .... mean 3.75

Note that only for case (c) are the mean and median equal. Normally this only occurs in cases, as above, where the distribution is symmetrical

Note/ The above text on the mean an median is courtesy of Lumsden, J."Elementary Statistical Method"Western Australia: University of Western Australia, 1974.

Average/Normal
Either the mean or median values according to the context.

Percentiles
Pertaining to percentage. Each of a series of values pertained by dividing a large number of quantities into a hundred equal groups in order of magnitude (courtesy of the Shorter Oxford English Dictionary).

Deciles
A tenth part

Median and Deciles

To calculate deciles, we divide the ranked dataset into ten parts. The median is simply that value which marks the level dividing the ranked dataset in half. For example 50 % of Januarys will have a total rainfall at or above the January median and 50% will have a total below. The median is also known as the 5th decile, decile 5 and the 50th percentile - they are all the same thing. Decile 9 or the 90th percentile for January, means that 90% of January totals will be at or below this figure. In other words there is a 90% chance of a January rainfall being at or below decile 9 (90th percentile), a 10% chance of it being above decile 9, and a 10% probability of it being below decile 1 (10th percentile). To get the annual decile value, you do not sum the deciles for the 12 individual months, but must calculate it separately. However it is possible for the two values to be the same by chance.

Prediction terms used

Median
It is the value above and below which lie half the scores in a distribution. It belongs to the general class of point statistics. See the example given above for the difference between mean and median. The words 'median' and 'average' may be interchanged because they will often equate to similar amounts of rainfall, particularly in the southern states.

Below average
The National Climate Centre uses the words "below average" in its seasonal outlooks to indicate below median seasonal rainfall or temperature values. This is a value in the lower half of values (by count of years). The word 'average' is used here to mean "what usually happens" and is not the arithmetic mean.

Above average
The National Climate Centre uses the words " above average" in its seasonal outlooks to indicate above median seasonal rainfall or temperature values. This is a value in the upper half of values (by count of years).

The outlooks are usually prepared in terms of probability of exceeding the median (above average). Probabilities more than 50% mean that wetter conditions or warmer conditions are more likely, while probabilities less than 50% mean that drier conditions or cooler conditions are more likely. In all cases however, wetter/drier and warmer/cooler are relative to the median value at the location you're looking at.

For temperature, the mean (or arithmetic average) and median usually turn out to be quite close, but in some of the drier parts of Australia, the mean can be quite a bit higher (... than the median).