Types of Data in Statistics

9 Key excerpts on "Types of Data in Statistics"

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  eBook - PDF

  Introduction to Mathematical Literacy

  • Alberto D. Yazon(Author)
  • 2019(Publication Date)
  • Society Publishing

    (Publisher)

  The values of these variables involve a counted or measured value. Subtypes None. Discrete values are counts of things. Continuous values are measures, and any value can theoretically occur, limited only by the precision of the measuring process. Exam-ples Gender, a variable that has the categories of male and female. Academic major, a variable that might have the categories Eng-lish, Math, Science, and History, among others. The number of previous presidential elections in which a citizen voted a discrete numerical variable. The household income of a citizen who voted a continuous variable . Source: http://www.informit.com/articles/article.aspx?p=353170 5.5. TYPES OF STATISTICS Mainly, the statistics can be categorized into two type: descriptive and inferential statistics. Introduction to Mathematical Literacy 110 5.5.1. Descriptive Statistics There is a type of statistics which is known as descriptive statistics which probably appears to the mind of most of the people when they hear the word ‘statistics.’ The main aim in such kind of statistics is to describe. There are numerical measures which are used to describe the features of the set of data. Some number of items which belong to this portion of statistics which include: • The whole descriptions of the data such as the five-number summary. • The exploration of relationships as well as a correlation between the paired data. • The distribution of a data set that can be measured with either the range or standard deviation. • The presentation of statistical conclusions in graphical form. • Some measurements such as skewness and kurtosis. • The average, or the measure of the center of a data set which consists of the mean, median, mode, or midrange (Figure 5.2). Figure 5.2: Excess Kurtosis for beta distribution with alpha and beta ranging from 1 to 5. Source: https://commons.wikimedia.org/wiki/File:Excess_Kurtosis_for_Beta_ Distribution_with_alpha_and_beta_ranging_from_1_to_5_-_J._Rodal.jpg.

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  Statistical Quality Control

  Using MINITAB, R, JMP and Python

  • Bhisham C. Gupta(Author)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  3 Describing Quantitative and Qualitative Data 3.1 Introduction In all statistical applications, we collect sets of data. These sets could be small, containing just a few data points, or very large and messy, with millions of points or more. Not all data are of the same kind, and therefore not all data sets can be treated in the same manner. In this chapter, we intro- duce the classification of data into various categories, such as qualitative and quantitative, and apply appropriate graphical and numerical techniques to analyze them. Sometimes data sets contain data points that are erroneous and thus may not belong to the data set. These data points are commonly known as outliers. In this chapter, we apply a method that can detect such outliers so that they may be either corrected and included in the analysis or eliminated from the analysis. In certain applications, we are studying two characteristics of an individual or item, and we may be interested in finding any association between these characteristics; a measure of such association is introduced in this chapter. The concept of descriptive and inferential statistics is also introduced. Finally, we study some important probability distributions that are quite fre- quently used in the study of statistical quality control. 3.2 Classification of Various Types of Data In practice, it is common to collect a large amount of non-numerical and/or numerical data on a daily basis. For example, we may collect data concerning customer satisfaction comments of employees, perceptions of suppliers, etc. Or we may track the number of employees in various departments of a company, check weekly production volume in units produced or sales in dollars per unit of time, etc. However, not all of the data collected can be treated the same way, as there are different types of data.

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  Statistics

  Principles and Methods

  • Richard A. Johnson, Gouri K. Bhattacharyya(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  Each entry corresponds to the observation of a specified characteristic of a sampling unit. For example, a nutritionist may provide an experimental diet to 30 undernourished children and record their weight gains after two months. Here, children are the sampling units, and the data set would consist of 30 measurements of weight gains. Once the data are collected, a primary step is organizing the information and extracting a descriptive summary that highlights its salient features. In this chapter, we learn how to organize and describe a set of data by means of tables, graphs, and calculation of some numerical summary measures. □ 1. MAIN TYPES OF DATA Before introducing methods of describing data, we first distinguish between the two basic types: 1. Qualitative or categorical data 2. Numerical, quantitative, or measurement data When the characteristic under study concerns a qualitative trait that is only classified in categories and not numerically measured, the resulting data are called categorical data. Hair color (blond, brown, red, black), employment status (employed, unemployed), and blood type (O, A, B, AB) are but some examples. If, on the other hand, the characteristic is measured on a numerical scale, the resulting data consist of a set of numbers and are called measurement data. We will use the term numerical-valued variable or just variable to refer to a characteristic that is measured on a numerical scale. The word “variable” signifies that the measurements vary over different sampling units. In this terminology, observations of a numerical-valued variable yield measurement data. A few examples of numerical-valued variables are the shoe size of an adult male, daily number of traffic fatalities in a state, intensity of an earthquake, height of a 1-year-old pine seedling, the time spent in line at an automated teller, and the number of offspring in an animal litter.

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  Statistics with JMP

  Graphs, Descriptive Statistics and Probability

  • Peter Goos, David Meintrup(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  2 Data and its representation A microphone in the sidewalk would provide an eavesdropper with a cacophony of clocks, seemingly random like the noise from a Geiger counter. But the right kind of per- son could abstract signal from noise and count the pedestrians, provide a male/female breakdown and a leg-length histogram … (from Cryptonomicon, Neal Stephenson, p. 147) Data is a set of measurements of one or more characteristics or variables of some elements of a population, or of a number of objects generated by a process. Different types of variables can be measured. 2.1 Types of data and measurement scales Variables are classified according to the measurement scale on which they are mea- sured. Categorical or qualitative variables are measured on a nominal scale or on an ordinal scale. Quantitative variables are either measured on an interval scale or on a ratio scale. 2.1.1 Categorical or qualitative variables 2.1.1.1 Nominal variables Elements of a sample or a population can be classified using a nominal variable: the value of the variable places an element in a certain class or category. Examples of such variables are • gender (male/female), • nationality (Belgian, German, and so on), Statistics with JMP: Graphs, Descriptive Statistics, and Probability, First Edition. Peter Goos and David Meintrup. © 2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd. Companion Website: wiley.com/go/goosandmeintrup DATA AND ITS REPRESENTATION 9 • religion (Catholic, Protestant, and so on), and • whether or not one owns a car (yes/no). Sometimes it can be useful to assign labels, code numbers, or code letters, to the different classes or categories. For example, a Belgian person may be assigned the code “1”, a Dutch person the code “2”, a French person the code “3”, and a German person the code “4”. It is important to note that these figures do not imply any order and/or quantity.

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  Quantitative Techniques in Business, Management and Finance

  A Case-Study Approach

  • Umeshkumar Dubey, D P Kothari, G K Awari(Authors)
  • 2016(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  For example, the employees of a company may be classi-fied according to their monthly salaries. Since quantitative data is characterised by differ-ent numerical values, the data represents the values of a variable. Quantitative data may be further classified into one or two types: discrete or continuous. The term discrete data refers to quantitative data that is limited to certain numerical values of a variable, for example the number of employees in an organisation or the number of machines in a factory. 2.5 Data Collection 2.5.1 Population This is the entire collection of entities that a manager is trying to study. 2.5.2 Sample This is a fraction of the population that represents the entire population in its characteris-tics proportionately. For example, when a magazine conducts an opinion poll among 1000 individuals from all over India, with a view to know the general opinion of Indians towards politicians, then all Indians is the target population and 1000 individuals represent the population and is referred to as the sample. In another example, to estimate the potential market for a new innovation, managers in a research department may study 1000 consumers in a particular territory. The managers make sure that this sample contains the consumers belonging to all cross sections (income, religion, education and locality) of the society. 2.5.3 Testing the Validity of Data This is testing the data for adequacy and reliability, as it influences the quality of the final decision. Managers can pose the following questions: 1. Data origin? 2. Is the source reliable? 22 Quantitative Techniques in Business, Management and Finance 3. Does the data support or contradict the previous decisions? 4.

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  Exploring Data and Business Management: How Information Helps in Supervision

  • Richa Tiwari(Author)
  • 2023(Publication Date)
  • Society Publishing

    (Publisher)

  For example, a digital camera converts electromagnetic information to a string of numerical data. • Projection of Data: By the use of algorithms and other mathematical analysis tools, future projection of data can be done. For example, a marketer launches a new product, goes through analyzes in the market to predict an increase in the sales of the new product. Data Analysis: An Introduction 37 • Quantification of Qualitative Entities: Quantitative information is recorded in the form of unique numbers. For example, asking respondents of an online survey to share the likelihood of recommendation on a scale of 0–10. 2.2.2. Quantitative Data: Collection Method The data in the form of numbers is quantitative data. Mathematical and statistical analysis of the data can lead to establishing some conclusion from various sources. There are three main methods of collecting quantitative data: • Survey: Earlier, surveys were conducted using paper-based methods and now have gradually evolved into the online mediums. The closed-ended type forms a key type of survey as they are more effective in quantitative data collection. These questions may also include different options to answer which they think may be appropriate for a particular question survey. These are further integrated in collecting feedback from an audience that is larger than the conventional size. The risk factor about the surveys is that the responses collected must be such that they can be generalized to the entire population without significant discrepancies. Survey can be classified further on the basis of the time evolved as; • Longitudinal Studies: It is a type of observational research in which market researchers conduct a survey from a specific time period to another, i.e., over a considerable course of time, it’s called longitudinal survey. This sort of survey is often implemented for trend analysis or studies where the primary objective is to collect and analyze a pattern in a data.

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  Research, Evaluation and Audit

  Key steps in demonstrating your value

  • Maria J. Grant, Barbara Sen, Hannah Spring, Maria J. Grant, Barbara Sen, Hannah Spring(Authors)
  • 2014(Publication Date)
  • Facet Publishing

    (Publisher)

  CRAVEN & GRIFFITHS DATA ANALYSIS 161 Descriptive statistics Techniques for summarizing data, e.g. mean, median, mode frequency, range Techniques for making generalizations about the characteristics of population based on a sample, e.g. correlation, t-test, Chi-square, ANOVA Parametric statistical analysis, use with scale variable (interval/ratio) data, e.g. Pearsons R Non-Parametric statistical analysis, use with nominal or ordinal variable data, e.g. Spearman’s rank correlation coefficient Inferential (analytical) statistics Figure 9.4 Summary of different statistical approaches Whether you choose to undertake some statistical analysis yourself, or whether you collaborate with a statistician, the outcome of rigorous research design, sampling and appropriate statistical approach is rich evidence to support, explain or clarify the situation you have been researching. Analysing qualitative data Qualitative research generates text or words that need to be described and summarized in order to answer a question. It typically involves the seeking of patterns and relationships between various themes that have been identified, or to relate behaviour or ideas to the characteristics of the participants. Qualitative data comes in various forms, including interview transcripts, recorded observations, focus groups, ethnographic studies, texts and documents, diary entries or blogs (see Chapter 7). It should be noted that quantitative studies can also include some form of qualitative data, such as open-ended survey questions and semi-structured interviews, which will require analysis through qualitative approaches. Before analysis can commence, data collected will most likely have to be transcribed. This is particularly true of focus groups and interviews, where the session has usually been recorded in some way.

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  Statistics for Laboratory Scientists and Clinicians

  A Practical Guide

  • Anne McDonnell Sill(Author)
  • 2021(Publication Date)
  • Cambridge University Press

    (Publisher)

  II The Right Statistical Test for Different Types of Data 4 Analyzing Continuous Data Well, what kind of data do you have? This chapter focuses on guidance in selecting the appropriate statistical test depending on what type of data is being analyzed. Remember, data can be continuous, binary, ordinal, nominal, normally distributed, non- normally distributed, log-distributed, and so on (Chapter 2). Decisions must be based on a full understanding of the kind of data you have and your analytic objective. Conduct your preliminary analyses! Plot your data! Look at your data! Do you have outliers, skewness, errors? 4.1 Single Continuous Distribution Univariate analyses are used to explore single variables at a time. Types of univariate data analyses are: • mean (Section 1.5.1) • mode (Section 1.5.3) • range (Section 1.5.4) • interquartile range (Section 1.5.5) • skewness (Section 1.5.6) • kurtosis (Section 1.5.7) • frequency distributions (Section 1.6). These are just a few of the ways you can describe a single variable. Examples of these univariate statistics are available in Sections 1.5 through 1.7. 61 4.2 Visual Comparison of Two Continuous Variables Using Scatterplots Although not a statistical test, one important first step in visualizing your bivariate continuous data is in the form of scatterplots (see Chapter 10). Scatterplots, which may easily be performed in Excel, can provide a clear snapshot of whether or not variables are associated or completely disassoci- ated, such as weight vs. height, rain in inches vs. plant growth. When drawing a tight-fitting line through the scatter dots, meaning a line from which the dots are best fitted, a good correlation is one where the distance of the dots from the line is minimal (see Section 4.3.3 for more on correlations). In another example, plotting the results of Test A against Test B (Figure 4.1) shows that the values are linearly related, but their scales of increase vary on the x- and y-axes.

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  Quantitative Techniques in Business, Management and Finance

  A Case-Study Approach

  • Umeshkumar Dubey, D P Kothari, G K Awari(Authors)
  • 2016(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  Kurtosis is the degree of peakness of a distribution of points; that is it measures the peakedness of a distribution. Two curves with the same central location and dispersion may have different degrees of kurtosis, that is curves with different Kurtosis but the same central location.

  2.14 Summary

  Statistical data is a set of facts expressed in quantitative form. The use of facts expressed as measurable quantities can help a decision maker to arrive at better decisions. Data can be obtained through a primary source or secondary source. When the data is collected by the investigator himself, it is called primary data. When the data has been collected by others, it is known as secondary data. A frequency distribution is the principal tabular summary of either discrete or continuous data. The frequency distribution may show actual, relative or cumulative frequencies. Actual and relative frequencies may be charted as a histogram, bar chart or frequency polygon. Two graphs of cumulative frequencies are less than ogive and more than ogive.

  Presentation of data is provided through tables and charts.

  REVIEW QUESTIONS

  1. Distinguish between primary and secondary data. Discuss the various methods of collecting primary data. Indicate the situations in which each of these methods should be used.
  2. Discuss the validity of the statement ‘A secondary source is not as reliable as a primary source’.
  3. Discuss the appropriateness of the methods of collecting data by
     1. Mailed questionnaire
     2. Personal interviews
  4. Explain the advantages of direct personal investigation compared with the other methods generally used in collecting data.
  5. Compare the different methods used in the collection of statistical data. Explain the importance of determining a statistical unit in the collection of data.
  6. Discuss the various sources of secondary data. Point out the precautions to be taken while using such data.
  7. Explain what precautions must be taken while drafting a useful questionnaire.
  8. As the personnel manager in a particular industry, you are asked to determine the effect of increased wages on output. Draft a suitable questionnaire for this purpose.

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