Thursday, September 29, 2022

# What Is Central Tendency In Math

## Measures Of Central Tendency Example

Central Tendency – Mean Median Mode Range – MathHelp.com

Let us understand the concept of the measures of central tendency using an example. The monthly salary of an employee for the 5 months is given in the table below,

 Month May $100 Suppose, we want to express the salary of the employee using a single value and not 5 different values for 5 months. This value that can be used to represent the data for salaries for 5 months here can be referred to as the measure of central tendency. The three possible ways to find the central measure of the tendency for the above data are, Mean: The mean salary of the given salary can be used as on of the measures of central tendency, i.e., x = /5 =$102.

## The Athenians Wall Conquest

In Greek history, records of the Athenians have shown them using a form of estimation to climb over their enemies fortress walls. To get into the forts of their enemies, Athenians would construct ladders with sufficient height to reach the top of their walls. However, to find the right height, they had their men count the number of bricks in a column of a wall.

Naturally, given the conditions, they returned with many different answers. While naturally some was wrong, it was accepted that the majority had to be right. In this case, we can see an implicit use of mode. The Athenians assumed that the most frequent value had to be correct. This was true even if none of the values represented more than half of the men.

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## What Is Central Tendency

Central tendency is a descriptive summary of a dataset through a single value that reflects the center of the data distribution. Along with the variability of a dataset, central tendency is a branch of descriptive statistics.

The central tendency is one of the most quintessential concepts in statistics. Although it does not provide information regarding the individual values in the dataset, it delivers a comprehensive summary of the whole dataset.

## Definition Of Measures Of Central Tendency

Comparing Measures of Central Tendency (1 of 2: Mean & Mode)

The Measures of Central tendency are numerical descriptive measures that indicate or locate the center of distribution or set of data. For instance, In a class of 50 students, the average height would be the average height of the class as a whole. Thus, It is also defined as a single value used to describe the center of data.

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## Skewed Distributions And The Mean And Median

We often test whether our data is normally distributed because this is a common assumption underlying many statistical tests. An example of a normally distributed set of data is presented below:

When you have a normally distributed sample you can legitimately use both the mean or the median as your measure of central tendency. In fact, in any symmetrical distribution the mean, median and mode are equal. However, in this situation, the mean is widely preferred as the best measure of central tendency because it is the measure that includes all the values in the data set for its calculation, and any change in any of the scores will affect the value of the mean. This is not the case with the median or mode.

However, when our data is skewed, for example, as with the right-skewed data set below:

We find that the mean is being dragged in the direct of the skew. In these situations, the median is generally considered to be the best representative of the central location of the data. The more skewed the distribution, the greater the difference between the median and mean, and the greater emphasis should be placed on using the median as opposed to the mean. A classic example of the above right-skewed distribution is income , where higher-earners provide a false representation of the typical income if expressed as a mean and not a median.

## When Should You Use The Mean Median Or Mode

The 3 main measures of central tendency are best used in combination with each other because they have complementary strengths and limitations. But sometimes only 1 or 2 of them are applicable to your dataset, depending on the level of measurement of the variable.

• The mode can be used for any level of measurement, but its most meaningful for nominal and ordinal levels.
• The median can only be used on data that can be ordered that is, from ordinal, interval and ratio levels of measurement.
• The mean can only be used on interval and ratio levels of measurement because it requires equal spacing between adjacent values or scores in the scale.
Levels of measurement

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## Finding The Mode For Continuous Data

In the continuous data below, no values repeat, which means there is no mode. With continuous data, it is unlikely that two or more values will be exactly equal because there are an infinite number of values between any two values.

When you are working with the raw continuous data, dont be surprised if there is no mode. However, you can find the mode for continuous data by locating the maximum value on a probability distribution plot. If you can identify a probability distribution that fits your data, find the peak value and use it as the mode.

The probability distribution plot displays a lognormal distribution that has a mode of 16700. This distribution corresponds to the U.S. household income example in the median section.

When to use the mode: Categorical data, Ordinal data, Count data, Probability Distributions

## Measures Of Central Tendency: Definition & Examples

A measure of central tendency is a single value that represents the center point of a dataset. This value can also be referred to as the central location of a dataset.

In statistics, there are three common measures of central tendency:

Each of these measures finds the central location of a dataset using different methods. Depending on the type of data youre analyzing, one of these three measures may be better to use than the other two.

In this post, well take a look at how to calculate each of the three measures of central tendency along with how to determine which measure is best to use based on your data.

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## Relation Between Arithmetic Mean And Median

When data in a set is evenly distributed, i.e. the difference between any two consecutive elements of the set is equal , then Median = Arithmetic Mean

For example, consider the numbers 3, 5, 7, 9, 11Difference between any two elements in the above set is 2. So, their median and mean must be equal. Lets check.Mean = /5 = 35/7 = 7Median = the middle value, which is 7.