On one hand, figures provide anchor to our statements, one the other, they can be manipulated to suit our needs. Photograph: (Getty)
By changing the mere representation of data, we can bend data to drive home our side of the argument
Today is World Statistics Day -- a day designated to remind us of the importance of numbers, figures, and data in our lives.
When we quote figures, it adds authenticity and gravity to what we are saying or writing. On the one hand, figures back up our statements but on the other, numbers can be manipulated to suit our needs. By changing the mere representation of the data, we can bend figures to drive home our side of the argument.
The following examples will make this clear:
For the same set of data, the average figures differ dramatically. (WION)
The above table shows the monthly salary of seven individuals. If one chooses mean as the tool for calculating the average salary, then it is easy to say that monthly salaries in the world are increasing. However, looking at other average figures, such as mode and median, a different picture emerges.
Pooja's salary of $1,000,000 skews the mean figure to a higher level.
Another example shows how different visualisations of the same data can mislead people
If the units are not mentioned on the axis, then the reader does not get a clear picture from the represented data. (WION)
Figure 1 does not say much as the unit is not mentioned on the y-axis. Does this graph represents width, volume, weight, height or something else?
Figure 2 represents weight on the y-axis, thus giving a meaning to the graphical representation. It shows the weight of apples from each individual. We can call this a fair graph.
The scale on the axis can change what one draws from the statistical representation. (WION)
Figure 3 represents the same data but the scale of the y-axis has changed, showing that the weight of apples with Joseph is much higher compared to the others.
Figure 4 again represents the same set of data but the scale of the y-axis has changed again. It appears that all three - Abdul, Rahul, and Joseph - have apples of the same weight with them.
By changing data visualisation, the magnitude of the statistics changes phenomenally. (WION)
In Figure 5, each apple equals 10 units. This is a fair representation, showing the weight of the apples taken from the farm of each individual.
Figure 6 distorts the data. To show the differences in the weights, this figure changes the height of each apple to represent the weight of the apples. It is a skewed representation which blows up the weight of apples from Joseph's farms.
There is another interesting example to explain how certain statistical representations can give the wrong picture.
It is often quoted that the average temperature of Oklahoma city is 60 degrees but this figure gives a wrong picture about the weather of the city. (WION)
One often hears that the average temperature of Oklahoma City is 60 degrees Fahrenheit. From hearing the average temperature, one may think Oklahoma City has the same balmy weather as California. However, a closer look at the figures will reveal that Oklahoma City actually has extreme weather. In summers its very hot and in winters it is very cold, far removed from the pleasant weather of California.
An upward sloping graph. (WION)
The above graph published in FORTUNE magazine displays the growth of a certain business. Looking at the graph, one may think that the company has experienced phenomenal growth over the years. But there are no figures mentioned on the y-axis. So, it can't be stated with certainty whether the said company added a few pennies each year to its growth or a few millions.
Thus, it is important to understand the importance of numbers and why one should be careful when using them. Numbers should give authentic information to people rather than misleading them.
We sign off with another set of weird statistics:
'Odds of being killed by falling out of bed: 1 in 2 million
Odds of being killed in a plane crash: 1 in 25 million'
Looking at this makes me think that I should find another place to sleep.