Frequency Distribution

7 Key excerpts on "Frequency Distribution"

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  eBook - ePub

  Quantitative Data Analysis with SPSS 12 and 13

  A Guide for Social Scientists

  • Alan Bryman, Duncan Cramer(Authors)
  • 2004(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, that is, relative frequency. In Table 5.2, the number 11 is the frequency relating to the arts category, that is, 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 SPSS will be addressed in a later section, but in the meantime it should be realised 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 summarised 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

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  Quantitative 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

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  Statistical Aspects of the Microbiological Examination of Foods

  • Basil Jarvis(Author)
  • 2008(Publication Date)
  • Academic Press

    (Publisher)

  Example 2.1 , the calculated mean value was 0.983 g and the standard deviation was ±0.0287 g.)

  TYPES OF Frequency Distribution

  Mathematically defined Frequency Distributions can be used as models for experimental data obtained from any population. Assuming that the experimental data fits one of the models then, amongst other things:

  1. The spatial (ecological) dispersion of the population can be described in mathematical terms. 2. The variance of population parameters can be estimated. 3. Temporal and spatial changes in density can be compared. 4. The effect of changes in environmental factors can be assessed.

  The mathematical models used most commonly for analysis of microbiological data include the Normal (Gaussian), Binomial, Poisson and Negative Binomial distributions, which are described below. The parameters of the distributions are summarized in Table 3.2 .

  TABLE 3.2 Some Continuous and Discrete Distribution Functions

  a The Normal distribution is the limiting form of the Binomial distribution when n → ∞ and p → 0.

  b Limiting form of binomial, as p → 0, q → ∞.

  STATISTICAL PROBABILITY

  Probability is about chance and the likelihood that an event will, or will not, occur in any specific situation. For instance, the probability that a specific person will win the jackpot in the National Lottery is very low (about 1 in 14 million) because the odds against are most improbable – yet people do win the Lottery showing that no matter how improbable an event there is always a chance that it will occur. By contrast, the chance of getting snow in winter if you live in Norway, Russia or Canada is very high – one might say it is certain to occur – but if you live in England the chance is not very high.

  If a normal coin is tossed once it will fall to show either a ‘head’ or a ‘tail’ and there is a 50% probability for obtaining a head (or a tail) in a single throw. This is written p = 0.50, q = 0.50 where (p + q ) = 1; p is the probability that an event will occur (i.e. of obtaining a ‘head’) and q

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  Statistics for the Behavioural Sciences

  An Introduction to Frequentist and Bayesian Approaches

  • Riccardo Russo(Author)
  • 2020(Publication Date)
  • Routledge

    (Publisher)

  2  Descriptive statistics

  2.1 Organising raw data

  When data are collected, they can initially look quite messy and unorganised, thus difficult to interpret. As indicated in the previous chapter, some order needs to be imposed on raw data if we want to extract useful information from them. Several techniques are available to display data in a concise way and to organise them in a clear manner. Some of the most common and useful techniques for plotting data will be described in this chapter.

  2.2 Frequency Distributions and histograms

  First, let us consider some hypothetical data collected in a naming task. A sample of 40 4-year-old children is presented with a series of 50 pictures depicting everyday objects. Their task is to name the objects represented in each picture, and the number of correctly named pictures is recorded for each child. The raw data are presented in Table 2.1 . A useful way to organise these data would be to record the frequency of occurrence of each score in the dataset. In a Frequency Distribution table, the scores are usually ranked from the lowest to the highest, and the number of occurrences of each score is given. Table 2.1 also includes the frequencies of the observed scores obtained by the sample of 4-year-old children in the naming task. The cumulative frequency and the percentage cumulative frequency of the scores are also given. The cumulative frequency of the scores is useful since it reveals the number of observations falling at or below (or above) a given score. The percentage cumulative frequency of the scores is also useful since it can be used to obtain the percentage of observations falling at or below a given score.

  Table 2.1 Hypothetical raw data on the number of pictures named in a sample of 40 4-year-old children. Their Frequency Distribution is also provided

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  Statistics for the Behavioural Sciences

  An Introduction

  • Riccardo Russo(Author)
  • 2004(Publication Date)
  • Psychology Press

    (Publisher)

  Chapter 2 Descriptive statistics

  Organising raw data

  When data are collected, they can initially look quite messy and unorganised, and hence difficult to interpret. As indicated in the previous chapter, some order needs to be imposed on raw data if we want to extract useful information from them. Several techniques are available to display data in a concise way and to organise them in a clear manner. Some of the most common and useful techniques for plotting data will be described in this chapter.

  Frequency Distributions and histograms

  First let us consider some hypothetical data collected in a naming task. A sample of 40 4-year-old children are presented with a series of 50 pictures depicting everyday objects. Their task is to name the objects represented in each picture, and the number of correctly named pictures is recorded for each child. The raw data are presented in Table 2.1 . A useful way to organise these data would be to record the frequency of occurrence of each score in the data-set. In a Frequency Distribution table the scores are usually ranked from the lowest to the highest, and the number of occurrences of each score is given. Table 2.1 also includes the frequencies of the observed scores obtained by the sample of 4-year-old children in the naming task. The cumulative frequency and the percentage cumulative frequency of the scores are also given. The cumulative frequency of the scores is useful since it reveals the number of observations falling at or below (or above) a given score. The percentage cumulative frequency of the scores is also useful since it can be used to obtain the percentage of observations falling at or below a given score.

  From the Frequency Distribution table it can be easily seen what are the lowest and the highest naming scores (i.e., 12 and 42 respectively), and what is the most common score (i.e., 26). Using the cumulative frequency column it can be seen that 10 children could name 21 pictures or less. From the percentage cumulative frequency column it can be observed that a score of up to and including 21 was obtained by 25 per cent of the children assessed.

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  Statistics

  The Essentials for Research

  • Henry E. Klugh(Author)
  • 2013(Publication Date)
  • Psychology Press

    (Publisher)

  Family size, number of parking tickets, and number of siblings are discrete variables. Unfortunately this distinction can become a bit blurred when we apply it to achievement test scores. If a test has 50 items, it would appear that we have a discrete variable; you can get 39 right or 40 right but not 39.126 right. However, we usually treat test scores as if they were continuous variables. We assume that instead of measuring achievement with a 50-item test we could have used a 500-item test or a 5000-item test so that we could, in theory, have an infinitely dividable continuous scale. We will say more about this issue a bit later. 2.4 Frequency Distributions Regardless of the scale of measurement used, the data from an experiment must be presented in an orderly fashion. Suppose we wish to compare the effectiveness of two different methods of instruction. We may have test scores from one group of students taught by the lecture method and another group taught by the discussion method, and we may wish to compare the two sets of scores. The data may be compared more easily if we first tabulate the scores into two Frequency Distributions. A Frequency Distribution is a listing of all the different score values in order of magnitude with a tally or count of the number of scores at each value. Table 2.2 shows two Frequency Distributions that might result if our data were presented in this form. Table 2.2 Frequency Distributions of Examination Scores for Students Taught by Lecture and by Discussion Methods With the scores pictured as they are in Table 2.2 we can see some differences between the distributions. The lecture method seems to produce higher achievement, but the range of scores is about the same. We can also observe that the scores of the lecture students tend to be concentrated toward the top of the distribution, while the scores of the discussion group seem to be more symmetrically distributed about a central value

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  Beginning Statistics with Data Analysis

  • Frederick Mosteller, Stephen E. Fienberg, Robert E.K. Rourke, Stephen E. Fienberg, Robert E.K. Rourke(Authors)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  FrequencyDistributions

       1

                 

  Learning Objectives

  1. Reaping the benefits from organizing data and displaying them in histogram form

  2. Gaining skill in interpreting frequency histograms

  3. Constructing a cumulative frequency diagram

  4. Finding quartiles from a cumulative graph

  1-1 DATA: AN AID TO ACTION

  Much human progress grows from the practice of keeping and analyzing records. Important examples are the records leading to the calendar, an appreciation of the seasons, the credit, banking, and insurance systems, much of modern production processes, and our health and medical systems. We shall, therefore, begin by explaining how to organize, display, and interpret data.

           What does this book do? This text primarily equips the reader with the skills

  1. to analyze and display a set of data,

  2. to interpret data provided by others,

  3. to gather data,

  4. to relate variables and make estimates and predictions.

  ORGANIZING DATA: THE USE OF PICTURES

  Data often come to us as a set of measurements or observations along with the number of times each measurement or observation occurs. Such an array is called a Frequency Distribution.

           To display a Frequency Distribution and disclose its information effectively, we often use a type of diagram called a frequency histogram. Let us look at some histograms. Examples 1 and 2 suggest some benefits we get from organizing data and displaying them in histogram form.

  EXAMPLE 1 Allocation of police. The chief of police of New York City has enlisted as many men as his budget permits. He has divided his forces about equally to cover three daily shifts; the first shift runs from midnight until 8 A.M., the second from 8 A.M. until 4 P.M., and the third from 4 P.M. until midnight. This system is bringing many complaints, and it is clear that during certain hours of the day the police calls require more police than are available. The chief selects a certain Sunday in August as a guide to action and makes a histogram (Fig. 1-1

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