Business Statistics

Business Statistics

Whether they are called quantitative methods, econometrics, psychological or business statistics, statistical methods are an indispensable tool in many scientific endeavors. Statistics are profusely used in business, while econometrics is a whole field that applies mathematical and statistical techniques to economic reality. Statisticians’ methodology is used extensively in financial analyses, marketing and even accounting.

A sample is a subset of a larger population that is supposed to accurately estimate some aspect of the population. A characteristic referring to the sample is called a statistic, while its population counterpart is a parameter (easy to remember since the words share the first letter in both cases). By convention, capital N refers to population while lower case n describes the sample. Random sampling, in which every item has an equal chance of being selected, is usually considered a prerequisite to unbiased reliable results.

Descriptive and Inferential Statistics

Data values can be quantitative or qualitative (categorical). Further, qualitative data can be subdivided into non-numeric and numeric, such as when each response, for example undergraduate business major, is assigned a number (finance – 1, marketing – 2, economics – 3, and so on). Both numeric and non-numeric can be nominal and ordinal. Quantitative data, in turn, can only be numeric but is subdivided into interval and ratio. Temperature would be interval, while age corresponds to ratio because someone who is 60 years old is exactly twice as old as a 30-year-old, but 10 degrees does not necessarily represent double the warmth of 5 degrees. The ratio versus interval is perhaps the most confusing of statistical concepts at an introductory course level.

Data

Many of the pictorial representations of statistics fall into the following common categories: pie chart, histogram, bar graph plus stem and leaf display. As mentioned above, the finance industry uses statistics to determine such items as price earnings ratios and dividend yields. Testing of theories such as arbitrage pricing also involves the fields of financial mathematics and financial econometrics. Excel is an excellent program to create charts. To create a stock chart in Excel one must know volume traded, opening and closing, as well as high and low, prices. Below are some examples of different displays using the software.

Graphs

The main visual difference between a histogram and a bar graph is that in a histogram columns touch, whereas in a bar graph they do not. Percentages are usually depicted in a pie chart, while for relative quantitative, relative categorical and cumulative frequencies, histograms, bar charts and ogives, respectively, are preferred.

Pie Chart

To draw a pie chart manually one must multiply the percentage of an element by 360 degrees. Thus, a 25% A would take 0.25  360= 90 degrees in the circle. Pie charts are often used in business for their clarity and impact. A marketing survey enquiring how many television sets households own may present their findings in this way (i.e. relative percentages of no TVs, 1 TV, 2 TVs, and 3 TVs).

Line Graphs

Of the examples provided here, the scatter plot is most similar to the line graph. The scatter plot contains dots corresponding to, usually, two variables (X and Y) and their interrelation is demonstrated by the regression, or best fit, line. If X and Y move in the same direction (as X increases, Y increases) they are said to be positively correlated, if their movements are reversed (as X increases, Y decreases or as X decreases, Y increases) then they are negatively correlated. Also, one never hears enough of this sentence: a correlation does not guarantee a causal effect.

In a corporate style presentation, a line graph would most likely be used to compare the fluctuation of the average price of gasoline and alternative energy sources (for instance Diesel, Regular, Premium and say Ethanol). None of the data in the pictures presented here is real; it is hypothetical, for illustrative purposes only. Conversely, a scatter plot may signify the relationship between average stay at a resort and food consumed (positive correlation) or price and quantity purchased (as price goes up, quantity goes down).

Stem & Leaf Display

In a stem (left) and leaf (right) display, first digits constitute the stem and the rest form the leaf. Unless otherwise specified a leaf unit equals one. So for instance the following set [90, 92, 92, 94, 97, 97, 97, 98, 99] would be portrayed as such:

9 | 0 2 2 4 7 7 7 8 9

Measures of Central Location

MEAN – perhaps the best-known statistical concept, the average. The mean is written as X bar (bar on top) for the sample, and the lower-case Greek alphabet letter Mu for the population. The mean is calculated by summing up all individual observations, and then dividing the sum by the total number of observations. Although decidedly useful, the mean can hide part of the picture. For instance, if one finds the average salary of marketing professionals, one outlier who was immensely more successful than everyone else may distort the number.

MEDIAN – to locate the median, one must first arrange the data in ascending order and find the middle position (number of data points + 1 / 2). If the sample is even, then it is necessary to take the average of the two middle values. In the case described above (advertizing specialists’ income distribution), the median would render a better picture of the true state of affairs.

MODE – from the French word meaning fashion, it is simply the value that appears most often in a collection (pun intended) of values. There can be more than one mode, and the sample can consequently be called unimodal (1 mode), bimodal (2 modes) and multimodal (3 or more). A mode would likely be the best measurement choice for a cosmetics’ retailer trying to determine which color of lipstick the store should stock up