STATISTICS – DESCRIPTION AND SPREAD

It is good valuation practice to provide a descriptive analysis of sale or rental data for inclusion in the valuation report. Basic statistical analysis used as a descriptive tool is particularly useful in this regard. Statistics 1 covers the use of measures of central tendency and spread. This will be done by using an example:

EXAMPLE

The following are the residential sales analyzed in a suburb in which the subject comparable property is being valued:

SUBURB: Summerton
Number of sales: 19 $'000 250 300 350 350 400 400 400 450 450 450 500 500 600 650 700 750 1000 1200 1500

How should such data be included in the valuation report? A very effective method is to summarize it as a frequency distribution. The following commands shows how this is done using Excel spreadsheet commands:

PREPARING A FREQUENCY HISTOGRAM IN EXCEL

On spreadsheet:

1. Enter data to be analyzed
2. Enter bin values: 100 300 500 700 900 1100 1300 1500 1700 <Options><Analysis tools><Histogram>

Enter input range
Enter bin range
Enter output range
<Enter>

Excel will construct the following table showing the frequency values, cumulative totals and a histogram as a chart. If the pareto chart option is chosen an additional table will be constructed on the right of the frequency table:

TABLE 1

Bin Frequency Cumulative %
Bin Frequency Cumulative % 100 1 5.26% 300 9 47.37% 300 9 52.63% 500 4 68.42% 500 4 73.68% 700 2 78.95% 700 2 84.21% 100 1 84.21% 900 1 89.47% 900 1 89.47% 1100 1 94.74% 1100 1 94.74% 1300 0 94.74% 1500 1 100.00% 1500 1 100.00% 1300 0 100.00% 1700 0 100.00% 1700 0 100.00%

The subsequent pareto chart is shown in the diagram below. It is useful in that it shows the progressive accumulation of sale data from the highest column at the left to the lowest column at the right. The right hand table the is the pareto table in which the frequencies are ranked in ascending order, according to frequency.

EXCEL - TO SEE HISTOGRAM

<Window><Chart 1>


DIAGRAM 2



The distribution in diagram 2 is "non symmetrical" being "skewed" to the right. Histograms should be analyzed according to their deviation from the centre and shape.

RULES FOR HISTOGRAMS
  1. Classes must be even in width ie, the bins must have a constant range. In table 2 this is 200.
  2. Class size should be the correct size to show the overall trend. If it is too large or too small, the trend will be lost. A class which is too small will hide the information.
  3. Do NOT use 3D histograms and graphs. The 3D perspective makes the reading of information and visual interpretation much more difficult compared to the normal 2 dimensional histograms.
COMPARING WITH ANOTHER SUBURB: Williamville

The valuer considers that another suburb Williamville, is comparable with Summerton for valuation purposes. Sales from the two suburbs can be compared to see whether or not there is comparability between the 2 samples.

SALES FOR WILLIAMVILLE $'000 100 200 250 300 300 350 400 450 450 450 500 550 550 600 600 650 700 700 750 If above data results in the frequency histogram shown in the diagram below:



Although the diagrams for the two suburbs have a similar centre line, the sales for Williamville are more concentrated around the centre, that is, there is less spread. Prima facie, the mean value of the sales in Wikkiamville are more reliable than for Summerton. However, the use of stemplots is a better way to compare two sales data.

See stemplots

DESCRIBING DATA

Diagrammatic analysis is very useful and should be an integral part of the valuation report however, for further analysis, quantitative measures are required. The most common quantitative measures are the measures of centrality; MEAN, MEDIAN and MODE.

See mean

See median

See mode

MEASURES OF CENTRALITY FOR SUMMERTON AND WILLIAMVILLE

MEAN MEDIAN MODE SUMMERTON: 589.4 450 300-500
WILLIAMVILLE: 465.7 450 300-500

The 3 measures together provide a good description or analysis of the sale data. Although the means are substantially different the medians and modes are the same. Therefore, some other measure of central tendency would be necessary to further analyse the sets of data. Although the above measures are useful, measures of centrality do not measure spread or range. The following useful statistics add a great deal to the analysis by measuring the spread of the sale data around the mean.

See quartiles

MAXIMUM AND MINIMUM VALUES - THE RANGE

Adding MAXIMUM and MINIMUM values provides a very good picture of the spread of the data. For unsorted data these values can be readily found with the following spreadsheet commands: Excel: =MIN(cell addresses) =MAX(cell addresses) The range provides a good measure of spread and the valuer would feel more confident about using data with a small range than data with a high range. For the sales in Summerton:

RANGE = 1500 - 250 = 1250(000)

See box plot

See standard deviation

See Z scores



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