![]()
1
Characterizing and defining statistical data
ICEBREAKER: International cost of living
How do you compare the international cost of living? One way is to measure how much it costs to eat out. However, here the question comes up, what type of meal? The UK-based magazine The Economist has devised a simple innovative approach by comparing the price of a McDonald’s Big Mac hamburger in various countries worldwide. It uses this as a basis since most of us at some point have eaten a McDonald’s hamburger, wherever that may have been. This is a study and analysis that The Economist has been performing since 1986. Statistical data, in local currencies, for January 2012 is given in Table 1.0 for 44 different countries.
Using the $US currency exchange rate at this period and considering, for example, the BRIC countries, we note that the cost of living in Brazil is 35 percent higher than in the USA. However, it is 39 percent, 61 percent and 42 percent lower in Russia, India, and China respectively. If you are a globetrotter and a hamburger is your staple diet, you will learn that the worldwide average price of the hamburger is $US 3.59; half of the hamburgers cost more than $US 3.36; the price range of the hamburgers is $US 5.17; the most expensive hamburger is in Norway at $US 6.79; and the cheapest “hamburger” is in India at $US 1.62, though in India a hamburger is made from chicken and not beef!
It is these characteristics and properties of statistical data that are covered in this chapter.
Figure 1.0 The ubiquitous hamburger.
Table 1.0 Big Mac index: The Economist, January 14, 2012
Chapter subjects
- ✓ Types of data • Quantitative data • Qualitative data • Mix qualitative/quantitative data
- ✓ Central tendency • Arithmetic mean • Median • Mode • Midrange • Weighted averages • Questionnaires and weighted averages • Geometric mean • Politics and central tendency
- ✓ Dispersion • Data spread • Range • Variance • Standard deviation • Calculation of variance and standard deviation • Deviation about the mean Coefficient of variation • Quartiles • Percentiles
In God we trust; everyone else bring data
Mike Bloomberg, Mayor of New York, 2001–131
To characterize and describe people we use terms like tall, slim, small, blond, blue-eyed, intelligent, and the like. In this way we develop an image of the person in question. Similarly in business it is important to characterize and describe statistical data so that we can understand situations using perhaps average, range, median, standard deviation, mode, etc. Statistical data are a collection of information from which conclusions or logical decisions can be drawn. From the data benchmark values can be determined, which then provide a reference point such as the world average price of a hamburger as given in the icebreaker.
Types of data
A collection of data is a dataset where the concept of “set” arises from referring to a set of objects: a set of stamps, a set of coins, or a set of drawings. A dataset is also called a data array. Data may be quantitative, qualitative, or a combination qualitative/quantitative. A dataset may describe a population where all data values are included: the population of China, the hotel staff population, or the elephant population in Africa. If the dataset is not a population it is a sample of a population: the back office staff would be a sample of the hotel population, a blood sample, or a water sample from the Rhine river. Population values are often considered parameters whereas sample values are taken as variables.
Quantitative data
Quantitative data may be integer values, or wh...
