The best way to examine a large set of numerical data is first to organize and present it in an appropriate tabular and graphical format. The table below presents the total number of overtime hours worked for 30 consecutive weeks by machinists in a machine shop. The data displayed here are in raw form, that is, the numerical observations are not arranged in any particular order or sequence.
These raw data are not amenable even to simple reading and do not highlight any characteristic/trend, such as the highest, the lowest, and the average weekly hours. Even a careful look at these data does not easily reveal any significant trend regarding the nature and pattern of variations therein.
As such no meaningful inference can be drawn, unless these data are reorganized to make them more useful. For example, if we are to ascertain a value around which most of the overtime hours cluster, such a value is difficult to obtain from the raw data. Moreover, as the number of observations gets large, it becomes more and more difficult to focus on the specific features in a set of data.
Thus we need to organize the observation so that we can better understand the information that the data are revealing. The raw data can be reorganized in a data array and frequency distribution. Such an arrangement enables us to see quickly some of the characteristics of the data we have collected. We can better organize the data by arranging it in ascending order in the form of an array.
What is an Array in Statistics?
When a raw data set is arranged in order, from the smallest to the largest observation or vice versa, the ordered sequence obtained is called an ordered array.
We now list out some of the advantages and disadvantages of displaying data in the form of an array.
Advantages of Ordered Array:
- It provides a quick look at the highest and lowest observations in the data within which
individual values vary.
- It helps in dividing the data into various sections or parts.
- It enables us to know the degree of concentration around a particular observation.
- It helps to identify whether any values appear more than once in the array.
Disadvantages of Ordered Array:
- In spite of various advantages of converting a set of raw data into an ordered array, an
array is a cumbersome form of presentation which is tiresome to construct.
- It neither summarizes nor organizes the data to present them in a more meaningful way.
- It also fails to highlight the salient characteristics of the data which may be crucial in terms of their relevance to decision-making.
Fundamentals of Business Statistics – JK Sharma