Frequency, Frequency Tables and Levels of Measurement
Frequency refers to the number of times a particular value occurs in a dataset. Frequency tables organize this information by listing the values and their corresponding frequencies. Levels of measurement categorize data as nominal, ordinal, interval, or ratio, based on the nature of the values being measured.
8 Key excerpts on "Frequency, Frequency Tables and Levels of Measurement"
eBook - ePubIBM SPSS for Introductory Statistics
Use and Interpretation
- George A. Morgan, Karen C. Barrett, Nancy L. Leech, Gene W. Gloeckner(Authors)
- 2019(Publication Date)
- Routledge(Publisher)
...CHAPTER 3 Measurement and Descriptive Statistics Frequency Distributions Frequency distributions are critical to understanding our use of measurement terms. We begin this chapter with a discussion of frequency distributions and two examples. Frequency tables and distributions can be used whether the variable involved has ordered or unordered levels or values. In this section, we only consider variables with many ordered values. A frequency distribution is a tally or count of the number of times each score on a single variable occurs. For example, the frequency distribution of final grades in a class of 50 students might be 7 As, 20 Bs, 18 Cs, and 5 Ds. Note that in this frequency distribution most students have Bs or Cs (grades in the middle) and similar smaller numbers have As and Ds (high and low grades). When there are a small number of scores for the low and high values and most scores are for the middle values, the distribution is said to be approximately normally distributed. We discuss this distribution and the normal curve later in this chapter. When the variable is continuous or has many ordered levels (or values), the frequency distribution usually is based on intervals of values for the variable. For example, the frequencies (number of students), shown by the bars in Fig. 3.1, are each for a range of scores. (In this case the SPSS program selected a range of 50: 250–299, 300–349, 350–399, etc.) Notice that the largest number of students (17 and 24) had scores in the middle two bars of the range (450–499 and 500–549). Similar small numbers of students have very low and very high scores. The bars in the histogram form a distribution (pattern or curve) that is similar to the normal, bell-shaped curve. Thus, the frequency distribution of the SAT math scores is said to be approximately normal. Fig. 3.1. A grouped frequency distribution for SAT mathematics scores. Fig. 3.2 shows the frequency distribution for the competence scale...
eBook - ePub- Louise Clark(Author)
- 2014(Publication Date)
- Research & Education Association(Publisher)
...CHAPTER 2 DESCRIPTIVE STATISTICS 2.1 FREQUENCY DISTRIBUTIONS AND GRAPHS/CHARTS A frequency distribution is one method of condensing original data into a more usable form. It is a table which is used to summarize a set of data by showing the number of items contained in the individual categories set forth in the table. A frequency distribution may be constructed using either qualitative or quantitative data. Qualitative data are much easier to tabulate in this manner due to the natural categorization of the data. a) Qualitative Data Frequency distributions illustrating qualitative data simply indicate the categories into which the data are to be divided and the number (or percentage) of the objects falling within each category. EXAMPLE: FREQUENCY DISTRIBUTION OF THE NUMBER OF STUDENTS ENROLLED IN XYZ UNIVERSITY BROKEN DOWN BY CLASS 1989 – 90 Charts or graphs are also meaningful data reduction techniques. The two most appropriate charts for qualitative data are the bar chart/graph and the pie chart. EXAMPLE: THE NUMBER OF STUDENTS ENROLLED IN XYZ UNIVERSITY BROKEN DOWN BY CLASS 1989 – 90 NOTE: It is also appropriate to present this data in a vertical bar chart. EXAMPLE: PIE CHART OF THE NUMBER OF STUDENTS ENROLLED IN XYZ UNIVERSITY BROKEN DOWN BY CLASS 1989 – 90 Note that the pie chart expresses the information as a percentage whereas the bar graph typically presents actual count. b) Quantitative Data When quantitative data are to be tabulated into frequency distributions, we must determine: 1. The number of non-overlapping classes required for the quantity of data being tabulated; 2. The size of each class (class width); and, 3. The beginning and ending points for each class (class limits). The steps required include: 1. Finding the first power of 2 that is greater than or equal to the number of data items being tabulated. This power of 2 will be the desired number of classes...
eBook - ePub- Perumal Mariappan(Author)
- 2019(Publication Date)
- Chapman and Hall/CRC(Publisher)
...The level of measurement is a function of the rules used to assign numbers and is an important aspect in determining what type of statistical analysis can be approximately applied to the data. 3.5.1 Nominal Scale The lowest or weakest level of measurement is the use of numbers to classify observations into mutually exclusive classes or groups. These observations are known as ‘nominal data’. Examples : Sex of the employee Male – 1 designates male Female – 2 designates female Parts produced by a machine Effective – 1 Defective – 2 Weight Overweight – 1 Normal weight – 2 Underweight – 3 It is also referred to categorical data. This is because the nominal variables identify categories of observations. 3.5.2 Ordinal Scale When observations are ranked so that each category is distinct and stands in some definite relationship to each of the other categories, the data are called ‘ordinal data’. Example : Product by people *Good quality product *Average quality product *Poor quality product 3.5.3 Interval Scale When the exact distance between any two numbers on the scale is known and when the data meet all the other requirements of ordinal data, they can be measured as interval data. Example : Two measures of temperature like Celsius and Fahrenheit. F = (9 / 5) * C + 32 The 0 point for each scale is different temperatures, and the unit measure is different for each, but there exists a fixed relationship. 3.5.4 Ratio Scale When measurements, having all the characteristics of the interval scale, also have a true 0 point, they have attained the highest level of measurement and are called ‘ratio data’. Examples : • The weight of an object may be measured in grams, ounces, or other measures. • The origin of each item is the same and is 0 weight. • The distance between 2 places may be measured in miles and. kilometres. 3.6 Frequency Number of times a value repeats itself is called the ‘frequency’...
eBook - ePubStatistics
The Essentials for Research
- Henry E. Klugh(Author)
- 2013(Publication Date)
- Psychology Press(Publisher)
...In this form the different values are arranged from highest to lowest, and a tally (or count) of each value is recorded. Once this has been accomplished, graphs can be constructed. Graphs are typically constructed with the abscissa or horizontal axis, representing the values of the scores or measurements, and the ordinate representing their frequency. The histogram (Figure 2.4) is a type of graph constructed of adjacent vertical bars; the height of the bar represents the frequency with which the score occurred. The frequency polygon is a closed figure drawn by connecting points plotted above the midpoints of the score intervals which are located along the abscissa. The distance of the points above the abscissa represents the frequency of the score’s occurrence. A measurement is assumed to occupy an interval and this interval extends one-half unit of measurement above and below the score. These are called the theoretical limits of the score interval. When many different measurements are obtained, it is often convenient to group several adjacent score intervals together. Such grouping intervals have score limits determined by the highest and lowest scores in them, and theoretical limits determined by the theoretical limits of these same scores. The grouped intervals must be mutually exclusive. The preference is to use 5 or 10 of the original score intervals to form the new grouped intervals, and to choose a value for this interval size (i) which will result in enough new grouped intervals to accurately depict the distribution. Grouping should proceed so that the lowest score in an interval is an even multiple of i. Such a grouping of score units into intervals, and the tally of measurements within these separate intervals, yields a grouped frequency distribution. Data may also be graphed in the form of a cumulative frequency curve or a cumulative proportion curve (Figure 2.6)...
eBook - ePubUnderstanding Political Science Statistics
Observations and Expectations in Political Analysis
- Peter Galderisi(Author)
- 2015(Publication Date)
- Routledge(Publisher)
...We make our choices based on several fundamental criteria. Each can be considered a constraining device, narrowing down our options of choice. The first constraining device is the level of measurement, or mathematical precision with which data are collected. What are the mathematical assumptions we can make? What mathematical rules can apply, and what manipulations can we perform? Statistics are mathematical summary tools. We need to be careful that our manipulations of the data do not go beyond what the data have to offer mathematically. All collection methods allow our cases or units of analysis (people in surveys, countries in comparative analyses) to be placed into different categories of a particular variable. The general rules for the creation of categories are that the categories are clearly mutually exclusive (i.e., distinctly different from each other—we should have no trouble deciding in which category to place any case), exhaustive (all possibilities are included—no cases are left out), and fairly parsimonious (although we lose information in the process, we generally try to limit the number of categories to those essential for maintaining conceptual diversity, or to guarantee sufficient case sizes for useful analysis, particularly when we are trying to generalize from a small sample). These rules apply to all levels of mathematical precision. Data can be collected and measured with differing levels of mathematical precision. There are three basic levels: nominal (sometimes called qualitative), ordinal (ordered qualitative), and interval (continuous or quantitative). Nominal is the least precise; very few mathematical assumptions can be made about the data. Interval is the most precise. These levels are, in the language of computer operating systems, backwards compatible, both in measurement and application. If data can be mathematically assumed to be interval, they also automatically carry ordinal and nominal properties...
eBook - ePubQuantitative Data Analysis with Minitab
A Guide for Social Scientists
- Alan Bryman, Duncan Cramer(Authors)
- 2003(Publication Date)
- Routledge(Publisher)
...The idea of a frequency distribution is to tell us the number of cases in each category. By ‘frequency’ is simply meant the number of times that something occurs. Very often we also need to compute percentages, which tell us the proportion of cases contained within each frequency, i.e. relative frequency. In Table 5.2, the number 11 is the frequency relating to the arts category, i.e. there are eleven arts students in the sample, which is 20 per cent of the total number of students. The procedure for generating a frequency distribution with Minitab will be addressed in a later section, but in the meantime it should be realized that all that is happening in the construction of a frequency table is that the number of cases in each category is added up. Additional information in the form of the percentage that the number of cases in each category constitutes is usually provided. This provides information about the relative frequency of the occurrence of each category of a variable. It gives a good indication of the relative preponderance of each category in the sample. Table 5.2 provides the frequency table for the data in Table 5.1. Percentages have been rounded up or down to a whole number (using the simple rule that 0.5 and above are rounded up and below 0.5 are rounded down) to make the table easier to read. The letter n is often employed to refer to the number of cases in each category (i.e. the frequency). An alternative way of presenting a frequency table for the data summarized in Table 5.2 is to omit the frequencies for each category and to present only the relative percentages. This approach reduces the amount of information that the reader must absorb...
eBook - ePub- Debbie L. Hahs-Vaughn, Richard Lomax(Authors)
- 2020(Publication Date)
- Routledge(Publisher)
...2 Data Representation Chapter Outline 2.1 Tabular Display of Distributions 2.1.1 Frequency Distributions 2.1.2 Cumulative Frequency Distributions 2.1.3 Relative Frequency Distributions 2.1.4 Cumulative Relative Frequency Distributions 2.2 Graphical Display of Distributions 2.2.1 Bar Graph 2.2.2 Histogram 2.2.3 Frequency Polygon (Line Graph) 2.2.4 Cumulative Frequency Polygon 2.2.5 Shapes of Frequency Distributions 2.2.6 Stem-and-Leaf Display 2.3 Percentiles 2.3.1 Percentiles 2.3.2 Quartiles 2.3.3 Percentile Ranks 2.3.4 Box-and-Whisker Plot 2.4 Recommendations Based on Measurement Scale 2.5 Computing Tables, Graphs, and More Using SPSS 2.5.1 Introduction to SPSS 2.5.2 Frequencies 2.5.3 Graphs 2.6 Computing Tables, Graphs, and More Using R 2.6.1 Introduction to R 2.6.2 Frequencies 2.6.3 Graphs 2.7 Research Question Template and Example Write-Up 2.8 Additional Resources Key Concepts Frequencies, cumulative frequencies, relative frequencies, and cumulative relative frequencies Ungrouped and grouped frequency distributions Sample size Real limits and intervals Frequency polygons Normal, symmetric, and skewed. frequency distributions Percentiles, quartiles, and percentile ranks In the first chapter we introduced the wonderful world of statistics. We discussed the value of statistics, met a few of the more well-known statisticians, and defined several basic statistical concepts, including population, parameter, sample, statistic, descriptive and inferential statistics, types of variables, and scales of measurement. In this chapter we begin our examination of descriptive statistics, which we previously defined as techniques that allow us to tabulate, summarize, and depict a collection of data in an abbreviated fashion. We used the example of collecting data from 100,000 graduate students on various characteristics (e.g., height, weight, sex, grade point average, aptitude test scores)...
eBook - ePubIntroductory Probability and Statistics
Applications for Forestry and Natural Sciences (Revised Edition)
- Robert Kozak, Antal Kozak, Christina Staudhammer, Susan Watts(Authors)
- 2019(Publication Date)
- CAB International(Publisher)
...2 Descriptive Statistics Making Sense of Data In order to adequately monitor and manage natural resources, such as forests and rangelands, many very large data sets are compiled. The objective of this chapter is to explore the tools used to make data sets more comprehensible. By organizing variables into tables, charts and graphs, and by calculating numbers that best describe the characteristics of a variable of interest, managers can quickly get information about the natural resources for which they are responsible. 2.1 Tables Data, such as those presented in Table 1.1 (see Chapter 1), are called raw data. Even considering only one variable (e.g. diameter at breast height, or dbh), it is difficult to assess this listing of 50 observations of unprocessed data, let alone a larger data set of 5000 or more data points. One of the simplest ways to organize variables is to rank them in ascending or descending order. Ranking observations, as shown with the 50 dbh observations in Table 2.1, does not reduce the size of the data set and is usually used to describe data sets with smaller numbers of observations only. When the number of observations is large, a more powerful tool, known as the frequency distribution, is used to describe a variable. In frequency distributions, observations are grouped into classes, and the frequency of observations in each class are tallied and presented in tabular form. Depending on the nature of the variable being grouped, we distinguish between three types of frequency distributions: categorical, ungrouped and grouped frequency distributions. Categorical frequency distributions are used to place qualitative, ordinal or nominal level variables into specific categories. Table 2.2 shows the frequency of the trees from Table 1.1 (see Chapter 1) by crown class. Since crown class is a categorical variable, four discrete classes are used and the number of trees in each class is tallied...
