Basic Statistics

Introduction to statistics

The Word Statistics Meaning and Use

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The post is about “The Word Statistics Meaning and Use”.

The word statistics was first used by German scholar Gottfried Achenwall in the middle of the 18th century as the science of statecraft concerning the collection and use of data by the state.

The word statistics comes from the Latin word “Status” or Italian word “Statistia” or German word “Statistik” or the French word “Statistique”; meaning a political state, and originally meant information useful to the state, such as information about sizes of the population (human, animal, products, etc.) and armed forces.

itfeature.com The word Statistics

According to pioneer statistician Yule, the word statistics occurred at the earliest in the book “The Element of universal erudition” by Baron (1770). In 1787 a wider definition was used by E.A.W. Zimmermann in “A Political Survey of the Present State of Europe”. It appeared in the Encyclopedia of Britannica in 1797 and was used by Sir John Sinclair in Britain in a series of volumes published between 1791 and 1799 giving a statistical account of Scotland. In the 19th century, the word statistics acquired a wider meaning covering numerical data of almost any subject and also interpretation of data through appropriate analysis.

The Word Statistics Now a Day

Now statistics are being used with different meanings.

  • Statistics refers to “numerical facts that are arranged systematically in the form of tables or charts etc. In this sense, it is always used as a plural i.e. a set of numerical information. For instance statistics on prices, road accidents, crimes, births, educational institutions, etc.
  • The word statistics is defined as a discipline that includes procedures and techniques used to collect, process, and analyze numerical data to make inferences and to reach an appropriate decision in a situation of uncertainty (uncertainty refers to incompleteness, it does not imply ignorance). In this sense word statistic is used in the singular sense. It denotes the science of basing the decision on numerical data.
  • The word statistics refers to numerical quantities calculated from sample observations; a single quantity calculated from sample observations is called statistics such as the mean. Here word statistics is plural.

“We compute statistics from statistics by statistics”

The first place of statistics is plural of statistics, in second place is plural sense data, and in third place is singular sense methods.

In another way, the word Statistics has two meanings:

  • The science of data:
    In this sense, statistics deals with collecting, analyzing, interpreting, and presenting numerical data. Therefore, statistics helps us to understand the world around us by making sense of large amounts of information. Statisticians use a variety of techniques to summarize data, identify patterns, and draw wise conclusions.
  • Pieces of data:
    Statistics also refers to the actual numerical data itself, for example, averages, percentages, or other findings from a study. The real-life examples of statistics are: (i) unemployment statistics or (ii) crime statistics.

Most Common Uses of Statistics

The following are the most common uses of Statistics in various fields of life.

Business and Economics

  • Market Research: Understanding consumer behaviour, satisfaction, preferences, and trends.
  • Operations Management: Optimizing processes, inventory control, and quality control.
  • Financial Analysis: Evaluating investments, risk management, and financial performance.

Healthcare

  • Clinical Trials: Compare and Evaluate the effectiveness and safety of new treatments.
  • Epidemiology: Studying the occurrence and distribution of diseases.
  • Public Health: Identifying health risks and developing prevention strategies.

Social Sciences

  • Sociology: Studying social phenomena, such as inequality, crime, and education.
  • Psychology: Understanding human behaviour, personality, and cognition.
  • Political Science: Analyzing political behaviour, public opinion, and election outcomes.

Government

  • Policy Development: Making informed decisions based on data and evidence.
  • Economic Planning: Forecasting economic growth and trends.
  • Public Administration: Improving efficiency and effectiveness of government services.

Education

  • Educational Research: Evaluating teaching methods, curriculum, and student outcomes.
  • Testing and Assessment: Developing and analyzing standardized tests.
  • Student Data Analysis: Identifying trends and addressing educational disparities.

Science and Technology

  • Research: Designing experiments, collecting data, and analyzing results.
  • Data Analysis: Discovering patterns, relationships, and insights in large datasets.
  • Machine Learning: Developing algorithms that can learn from data and make predictions.

Sports

  • Player Performance Analysis: Evaluating athlete performance and identifying areas for improvement.
  • Team Strategy: Developing game plans and making tactical decisions.
  • Sports Betting: Analyzing data to predict game outcomes.

For learning about the Basics of Statistics Follow the link Basic Statistics

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Rules for Skewed Data Free Guide

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Introduction to Skewed Data: Lack of Symmetry

Skewness is the lack of symmetry (lack of normality) in a probability distribution. The skewness is usually quantified by the index as given below

$$s = \frac{\mu_3}{\mu_2^{3/2}}$$

where $\mu_2$ and $\mu_3$ are the second and third moments about the mean.

The index formula described above takes the value zero for a symmetrical distribution. A distribution is positively skewed when it has a longer and thin tail to the right. A distribution is negatively skewed when it has a longer thin tail to the left.

Any distribution is said to be skewed when the data points cluster more toward one side of the scale than the other. Creating such a curve that is not symmetrical.

Skewed Data

Skewed Data

The two general rules for Skewed Data are

  1. If the mean is less than the median, the data are skewed to the left, and
  2. If the mean is greater than the median, the data are skewed to the right.

Therefore, if the mean is much greater than the median the data are probably skewed to the right.

Misinterpretation of Mean and Median: The mean can be sensitive to outliers in skewed distributions and might not accurately represent the “typical” value. The median, which is the middle value when the data is ordered, can be a more robust measure of the central tendency for skewed data.

Statistical Tests: Some statistical tests assume normality (zero skewness). If the data is skewed, alternative tests or transformations might be necessary for reliable results.

Identifying Skewed Data

There are a couple of ways to identify skewness in data:

  • Visual Inspection: Histograms and box plots are useful tools for visualizing the distribution of the data. Skewed distributions will show an asymmetry in the plots.
  • Skewness Coefficient: This statistic measures the direction and magnitude of the skew in the distribution. A positive value indicates a positive skew, a negative value indicates a negative skew, and zero indicates a symmetrical distribution.

FAQs about Skewed Data

  1. What is the skewness of data?
  2. What is the lack of symmetry?
  3. What is a positive skewed distribution?
  4. What is a negative skewed distribution?
  5. How a skewness in data be identified?
  6. What is the assumption of different statistical tests?
  7. What is the visual inspection of data skewness?
  8. What is the use of the skewness coefficient?
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