Statistical Methods Influencing Decision Making

Statistics is defined as the scientific practices and methods of collecting, organizing, presenting, analyzing and interpreting data to avail information that promotes effective decision-making (Lind, Marchal, & Wathen, 2015.). Data is the raw, usually disorganized details and numbers that can be used to conclude a given research question. Information, on the other hand, is processed data that has been organized, transformed, and presented in a way that is useful to the decision-making process.

Statistics has several key principles. First, the population is the entire set of individuals or objects from whence a given dataset is selected to answer a research question. On the contrary, a sample is a subset of data used to generalize an aspect of the population. A parameter is data about the entire population while a statistic is an inference about the population from a sample. A variable is a single qualitative or quantitative characteristic of the population that is measurable or countable. Qualitative variables are those that are recorded as non-numeric attributes, such as gender, skin color, race, and country of birth. In contrast, quantitative variables are those that have been recorded numerically, for example, age, bank balance, or number of deaths.

**Types of Statistics**

Statistics is either descriptive or inferential depending on the research queries to be answered and the nature of data that is available. The descriptive one involves the assembling, ordering, summarizing, and effectively presenting information to give insight into a situation. They allow deriving patterns from data but not make conclusions beyond the analyzed data. They are simple explanation of data offered inform of tables, charts, graphs, or statistical discussions of the research results, for example, the mean age of a group. Inferential statistics, on the contrary, uses samples from a given population to make statistical generalizations and estimations. An example is opinion pools using few citizens to predict a presidential outcome.

**Frequency Tables**

A frequency table is “a grouping of qualitative data into mutually exclusive and collectively exhaustive classes that show the number of observations in each class” (Laerd Statistics, 2018). Frequency is a measure of the how often a given value of a variable, for instance, the times a person between the age of 15 and 20 is shot in New York City occurs. Since a large population has a lot of values for a specific variable, statisticians using frequency tables often divide the values into groups called class intervals (Mathsteacher.com, 2018). In an ideal situation, one should have between 5 to 10 classes for a given variable, meaning data is organized into value ranges. For example, with a sample of 1000 people of different races with ages ranging from 18 to 108 years, one would have nine classes, each with an interval of 10 years and a frequency showing how many people in a given age bracket are from a given race.

**Numerical Descriptions of Quantitative Variables**

Quantitative variables are numerically described using the measures of location and measures of dispersion. The former, also called the central tendency, tries to describe data by identifying the central value within a given dataset. The dataset output is the summary statistics that describe a given population’s or sample’s mean, mode, and median. The mean is the average value of a given dataset calculated by adding the values of a variable and dividing them by the number of observations. It is either a sample mean if the observations are from a sample or a population mean if the observations are for the entire population. The mean uses all the data in a sample or population to model the data. The median arranges data with the order of magnitude and the middle value taken. Median is common when there are obvious outliers in a dataset that creates skewness that makes the mean to be less representative of the data centrality. The mode represents the most frequent value of a given dataset. For example, given a list of ages for a particular group as 10, 12, 10, 15, 8, the mean would be 11, the median would be 10, and the mode would be 10.in contrast, the measures of dispersion tries to describe the variability or spread in a given population or sample (Stark, 2005). Such a function is quite important as it tells how well the measures of location, especially the mean represents the population or sample allowing one to make sound decisions. The range is the easiest measure of dispersion that quantifies the difference between the maximum and the minimum values in a dataset (Lind, Marchal, & Wathen, 2015). It is a simple to measure mainly used to make decisions in production companies and control workers input.

Variance measures the average amount a population or sample deviates from its mean. Since the variance is a square of the units used to measure a population or sample variability, to obtain a standard unit same as the arithmetic mean, the standard deviation is adopted. Standard deviation is the square root of the variance. All these measures of dispersion give information that allows management to make key decisions in services delivery and products development.

**Displaying and Exploring Data**

Displaying data visually consolidates it and make it easily understandable. One way of displaying data is by using various types of graphs, such as bar, line, and histograms. Graphs summarize large numerical data by using an image to highlight various patterns in the dataset. Bar charts/graphs are drawn on a horizontal (x) axis and vertical (y) axis, which has a calibrated scale with units of measurement. They have vertical or horizontal bars whose heights vary proportionally to the size of data group represented. Similarly, line graphs are drawn on the x-axis and y-axis, and they indicate data that changes over time or comparative time change between variables. Dot plots are also used to explore data in a manner that is easy to understand by using small circles to indicate datasets that are continuous and quantitative. The distribution of points on the scale can be clustered at one point for close observations, or gapped for points that are far apart.

**Concepts of Probability**

Probability refers to the likelihood that an event will occur in the future and the frequency of its incidence. There exist several schools of thought on how to assign probability: classical, empirical, and subjective. The first one is based on the assumption that outcomes of an experiment are equally likely, for example, while rolling dice the probability that any face can appear on top is equal. The second view states that the probability of an event occurring is based on its frequency in the past (Lind, Marchal, & Wathen, 2015.). For example, the probability of a child falling off a bicycle depends on how many times he or she has had the accident in the past. The last concept states that the likelihood of an event happening is based on the information available, such as the estimation of football teams playing at world cup depending on the qualifiers list.

**Company Using Statistics to Make Business Decisions**

The Google Company uses statistics to drive its business operations. It implemented the people’s analytics to revolutionize its human resource department. The people-related decisions are based on data analytics. The firm uses its PiLab to conduct experiments on people and statistically analyze the best ways to manage them. From statistics, the PiLab reduced employee’s calorie intake by using data to reduce the size of plates (Sullivan, 2013). Furthermore, the enterprise developed an algorithm that predicts which new hires have the highest probabilities of being successful.

References

Laerd Statistics. “Measures of Spread | How and when to Use Measures of Spread | Laerd Statistics.” *SPSS Statistics Tutorials and Statistical Guides | Laerd Statistics*, 2018. statistics.laerd.com/statistical-guides/measures-of-spread-range-quartiles.php. Accessed 8 Sept. 2018.

Lind, Douglas A, et al. *Statistical Techniques in Business & Economics*. 16th ed., McGraw-Hill/Irwin, 2015.

Mathsteacher.com. “Frequency and Frequency Tables.” *Interactive Maths Series Software (interactive Mathematics Software or Math Software)*, 2018, www.mathsteacher.com.au/year8/ch17_stat/03_freq/freq.htm. Accessed 8 Sept. 2018.

Stark, Philip B. “Measures of Location and Spread.” *Sticigui: Statistics Tools for Internet and Classroom Instruction*, Department of Statistics. U of California, Berkeley, 2005, www.stat.berkeley.edu/~stark/SticiGui/Text/location.htm. Accessed 8 Sept. 2018.

Sullivan, John. “How Google Is Using People Analytics to Completely Reinvent HR.” *TLNT*, [New York], 26 Feb. 2013, www.tlnt.com/how-google-is-using-people-analytics-to-completely-reinvent-hr/. Accessed 8 Sept. 2018.