MEASURES OF CENTRAL TENDENCY COMPARISON
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 courses with a discussion of so-called descriptive statistics, no attempt is made to generalize.
That is, methods for summarizing large amounts of numerical data, their graphical representation, procedures for ‘fitting’ data to theoretical models, and so on. The goal of such procedures is to communicate the key features of a set of numbers to a colleague, for example. The assumption is that he does not want to be bothered with all of the facts that support your conclusion; this is a noble goal.
Furthermore, most descriptive statistics rules 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 after statistical inference. You will know what calculations to perform once you know what kind of interference you can make from a set of data. It reduces data to some form, usually a number that is easily comprehended.
A crucial statistical concept for learners is the data set as an entity, or developing 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 a focus on aggregates. Descriptive statistics include measures of central tendency. A typical value will be in the central region if the values are arranged in order of magnitude. This explains why the measure of location is sometimes called the measure of central tendency.
THE STUDY’S BACKGROUND
Measures of central tendency are also known as location or average measures. A value that is typical or representative of a set of data is referred to as an average. Because such typical values tend to cluster in the center of a set of data organized by magnitude. Almost everyone has used the word “average” at some point in their lives. By average, we usually mean 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 labor unions frequently quote what they consider to be the ‘average’ income of employees, with the employer’s usually being higher than the union’s, implying that the two parties are frequently speaking of two different averages generated from the same body of data. Because of the ambiguity and confusion surrounding the term “average.”
Measures of central tendency are commonly regarded as the most straightforward part of descriptive statistics because they deal with everyday events. The dominance of numerical methods for data comparison demonstrates a disregard for data distributional features.
The selection and collection of data, as well as the calculation of average numbers, are not difficult, but the use of terms such as houses (real objects) and living things appears to be difficult. The proliferation of statistical ideals in people reflects the increased emphasis on elementary level data analysis and statistics.
OBJECTIVE OF THE STUDY By the end of the study, we should be able to compare central tendency measures in relation to variance. With the help of variance, we would be able to determine which of the measures of central tendency is best used in.
SIGNIFICANCE OF STUDY At the conclusion of the research, its application in the physical world would motivate students to study and apply 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 private sector.
TERMS DEFINITION 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 center of a set of data arranged 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 common measures of central tendency.
The mode of a set of numbers is the most frequently 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 greater than or equal to it. In an array, is either the middle value or the arithmetic mean of the two middle values.
A set of numbers x1, x2,… xn’s arithmetic mean is their sum divided by n.
The geometric mean (G) of N positive numbers x1, x2,… xn is the nth root of the number product.
The harmonic mean (H) of a set of n numbers x1, x2,… xn is the reciprocal of the arithmetic mean of the numbers’ reciprocals.
A set of square numbers x1, x2,… xn’s quadratic mean is their sum 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 greater than or equal to their harmonic mean but less than or equal to their arithmetic mean.
The arithmetic mean of the squares of deviation from the mean of numbers is the variance of a set of numbers.