# Application of measures of central tendency. Application of Measures of Central Tendency and Variability 2022-10-16

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Measures of central tendency, also known as statistical averages, are used to summarize and describe the characteristics of a set of data. The three most common measures of central tendency are the mean, median, and mode. Each of these measures has its own unique characteristics and is used in different situations depending on the nature of the data.

The mean, also known as the average, is calculated by adding up all the values in a dataset and dividing by the number of values. The mean is a useful measure of central tendency when the data is continuous and follows a normal distribution, meaning that the majority of the values are clustered around the center and there are fewer extreme values. However, the mean can be affected by outliers, or extreme values that are much higher or lower than the majority of the data. This can cause the mean to be misleading, as it may not accurately represent the majority of the data.

The median is the middle value in a dataset when the values are arranged in numerical order. To find the median, the data must first be sorted from smallest to largest. The median is a useful measure of central tendency when the data is skewed or has outliers, as it is not affected by extreme values. The median is also useful when the data is ordinal, meaning that it is ranked or has categories, as it does not require the data to be continuous.

The mode is the most frequently occurring value in a dataset. The mode is a useful measure of central tendency when the data is categorical, as it represents the most common category. However, a dataset may have multiple modes, or no mode at all if no value occurs more frequently than the others.

Measures of central tendency are useful for summarizing and understanding large datasets. For example, a business may use the mean to determine the average salary of its employees, or the mode to determine the most popular product among its customers. In research studies, measures of central tendency are often used to report the results of experiments, as they provide a quick and easy way to understand the main findings.

In conclusion, measures of central tendency are useful tools for summarizing and describing the characteristics of a dataset. The mean, median, and mode are the three most common measures of central tendency, and each has its own unique characteristics and uses depending on the nature of the data. These measures are widely used in various fields to understand and analyze data, and are essential for making informed decisions and conclusions.

## Application: Measures of Central Tendency and Variability

Then we shall find out the value of fb and fp and substitute them in the formula. Read through it more carefully. Measures of central tendency and dispersion are vital tools to draw a short interpretation of data. For the measures of variation, the 1st sample, when compared to the other four samples using the coefficient of variation Standard deviation divided by the mean , has the highest variation. Consequently, 28 is the median of this dataset.

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## Measures Of Central Tendency And Dispersion

Illustration 12: Ordered Array of Unit Exam Scores Even number of scores Student Score 3 6 12 19 35 47 To determine the median of an even number of scores, we begin by adding the 2 middle numbers and dividing by 2. In the class interval in which 25 lies its lower limit will be taken. Crowthorne, Berkshire: Transport and Road Research Laboratory. Statisticians apply statistical thinking and methods to a wide variety of scientific, social, and business endeavors in such areas as astronomy, biology, education, economics, engineering, genetics, marketing, medicine, psychology, public health, sports, among many. What is strange to me is that the 3rd sample has a higher coefficient of variation, therefore more variation, than the 5th sample, even though the 3rd sample has an almost normal distribution. It can actually point you to understanding something new about your data.

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## Measures of Central Tendency and How It Helps in Educational Psychology

Thanks for the great question and good insight! Hey, Jim its Kechler thank you for your advice. Note: the median is most appropriate in the presence of outliers. On a display of the normal curve the median is exactly the midpoint of the data distribution and is located in the exact center of the graph. The mean is identified in a positively and negatively skewed data distribution as it generally relates to both the mode and the median. Advantages of Median: 1.

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## Business Applications Of Measure Of Central Tendency Example

In fact, a key idea in inferential statistics is that the specific sample a study draws from a population is only one of an infinite number of samples that it could have obtained. The wider the IQR, the greater the spread the data spread. Fortunately this is simple, as shown in Step 5. Our result is a sample mean because we are interested in finding the mean annual income of all secretaries on the basis of the annual income of a smaller sample consisting of only 6 secretaries. What is the mode for illustration 9? In the dataset with the odd number of observations, notice how the number 12 has six values above it and six below it.

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## Mean, Median, and Mode: Measures of Central Tendency

Mean versus median applet. The first quartile Q1 is a point below which 25% of numbers in the distribution lies. N stands for the total number of frequencies. The 2nd sample has 52 items, the 4th sample has 56 items, and the 5th sample has 42 items. Census Bureau, "median household income" is defined as "the amount which divides the income distribution into two equal groups, half having income above that amount, and half having income below that amount.

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## What is the Importance of Measures of Central Tendency in Statistics?

Here we say that the median is 9 because 3 scores are in the left and 3 on the right of it. Column fx is found by multiplying the mid-point x of each interval by the number of scores f on it; the mean 47. You can then better understand your data and how to analyze it. That is why; measures of central tendency are also called as measures of the first order. To prepare for this Assignment, review mean, median, and mode as well as the different types of distributions in your textbook.

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## Application of Measures of Central Tendency and Variability

For its determination, it is not essential to know the extreme items, provided the distribution is regular. In the examples below, I use whole numbers for simplicity, but you can have decimal places. If you measure parts repeatedly and the average or central tendency of the measurements are unbiased on target on average , you have an accurate measurement system. So, try a mix of the statistical tests that I recommend and investigations of the preparation method. From Illustration 7: Mode of a Normal Curve Note that the mode is located at the highest point of the graphed data.

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## American Board

The teacher then counts down or up to the 8 th score to determine the midpoint, or median. On a bar chart, the mode is the highest bar. It not only measures the central tendency or grouping of data, but it also provides a reference point to assist teachers in understanding the nature of the students and their needs, and then guides teachers in planning instruction that will meet their needs. Graphing is always important for understanding your data. The average of 27 and 29 is 28. Both cases are examples of non-normal data distributions.

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