MEASURES OF CENTRAL TENDENCY COMPARISON
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MEASURES OF CENTRAL TENDENCY COMPARISON
ABSTRACT
This study is focused on comparing measurements of central tendency. This is to discover the most appropriate metrics for average, employing variance for easy gathering of data of centrally situated middle integers. Data was collected to compute the various metrics of central tendency.
The variance for each distribution was then calculated using these measurements. According to this study, the arithmetic mean is the best measure of central tendency. As a result, it is widely suggested for use as a trustworthy sample mean for population.
CONTENTS TABLE
Introduction to Chapter One
The study’s context
Problems are listed below.
The investigation’s goal
The Importance of Research
Study limitations
Term definition
The second chapter is a review of the literature.
Methodology is the third chapter.
The manner
The average
The mathematical mean
The geometric average
The harmonic average
The quadratic average
Variance
Chapter four: Problem solved
5th chapter
Summary, conclusion, and advice
Summary
Conclusion
Recommendation
References
CHAPITRE ONE
STUDY BACKGROUND
One of the most important areas of statistics to study is descriptive statistics. It deals with the analysis, summarization, conclusions, and presentation of qualitative and quantitative data. This area is restricted to the information at hand. When beginning statistics classes with a discussion of so-called descriptive statistics, no attempt is made to generalise.
That is, methods for summarising large amounts of numerical data, their graphical representation, procedures for ‘fitting’ data to theoretical models, and so on. The goal of such techniques is to communicate the key properties of a group of numbers to a colleague, for example. The assumption is that he does not want to be troubled with all of the data that support your conclusion; this is a noble goal.
Furthermore, most descriptive statistics principles are dependent on what one wants to do with their data; few people collect data in order to summarize, support arguments, or draw inferences from them. If this is the case, descriptive statistics should be studied following statistical inference.
You will know what calculations to execute once you know what sort of interference you can make from a collection of data. It lowers data to some form, usually a number that is easily understandable.
A crucial statistical concept for learners is the data set as an entity, or gaining a statistical perspective. Keeping a statistical perspective necessitates focusing on the dataset as a whole rather than on individual data values. By concentrating on comparing measures of central tendency.
Would be given a conceptual structure that allows for an emphasis on aggregates. Descriptive statistics include measures of central tendency. A typical value will be in the centre zone if the values are ordered in order of magnitude. This explains why the measure of location is frequently called the measure of central tendency.
THE STUDY’S HISTORY Measures of central tendency are often known as location or average measures. A value that is typical or indicative of a set of data is referred to as an average. Because such typical values tend to cluster in the centre of a set of data organised by magnitude.
Almost everyone has used the word “average” at some point in their lives. By average, we usually imply the ‘normal position.’ For example, it is widely accepted that the ‘average’ age for starting primary school is between five and six years old. Employers and labour unions frequently quote what they believe to be the ‘average’ income of employees, with the employer’s usually being greater than the union’s, implying that the two sides are frequently speaking of two different averages obtained from the same body of data. Because of the vagueness and uncertainty around the term “average.”
SUMMARY OF THE PROBLEMMeasures of central tendency are commonly regarded as the most straightforward aspect of descriptive statistics because they deal with everyday happenings. The prevalence of numerical methods for data comparison demonstrates a disregard for data distributional properties.
The selection and gathering of data, as well as the calculation of average figures, are not difficult, but the use of terminology such as houses (actual objects) and living beings appears to be problematic. The prevalence of statistical ideals in people reflects the rising emphasis on elementary level data analysis and statistics.
OBJECTIVE OF THE STUDY By the completion of the study, we should be able to compare central tendency measures in respect to variance. With the help of variance, we would be able to determine which of the measures of central tendency is best suited in.
SIGNIFICANCE OF STUDY At the conclusion of the research, its implementation in the physical world would stimulate students to study and use it in real life situations.
This research aims to improve the teaching and learning of this subject in a higher education institution’s mathematics department. This is especially relevant in universities, polytechnics, and educational colleges. The study is also important to statisticians, academics, the government, and the corporate sector.
DEFINITION OF TERMS Measures of central tendency of a distribution are values that are typical or represent the data. Because such typical values tend to cluster in the centre of a set of data ordered by magnitude, averages are also known as measures of central tendency. The mode, median, and arithmetic mean, geometric mean, harmonic mean, and quadratic mean are the most prevalent metrics of central tendency.
The mode of a set of numbers is the most often occurring value. It might not exist, and if it does, it might not be unique. A distribution with only one mode is referred to as unimodal.
The median of a distribution is the number for which the distribution’s values less than or equal to it are the same as the values higher than or equal to it. In an array, is either the middle value or the arithmetic mean of the two middle values.
A collection of numbers x1, x2,… xn’s arithmetic mean is their total divided by n.
The geometric mean (G) of N positive values x1, x2,… xn is the nth root of the number product.
The harmonic mean (H) of a collection of n numbers x1, x2,… xn is the reciprocal of the arithmetic mean of the values’ reciprocals.
A collection of square numbers x1, x2,… xn’s quadratic mean is their total divided by n.
The following are the relationships between the Arithmetic mean, Geometric mean, and Harmonic mean: The geometric mean of a positive number set x1, x2, x3,… xn is larger than or equal to their harmonic mean but less than or equal to their arithmetic mean.
The arithmetic mean of the squares of variation from the mean of numbers is the variance of a collection of numbers.
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