# What are measures of central tendency variation and relationship

### Introducing Statistics towards Central Tendency Metrics, Correlation and Dispersion

what are called measures of central tendency and measures of variability. .. an idea, albeit an imperfect one, of an entity's standing in relation to some standard. A measure of central tendency (also referred to as measures of centre or central location) is a summary measure that attempts to describe a. The central tendency of a distribution represents one characteristic of a distribution. Another aspect is the variability around that central value. While measures of.

It approaches the mean calculated from the raw data as the number of intervals increase.

The irony in this is that most of the times this value never appears in the raw data. Repeated samples drawn from the same population tend to have similar means. The mean is therefore the measure of central tendency that best resists the fluctuation between different samples.

Even though mean can be calculated for numerical ordinal data, many times it does not give a meaningful value, e. Weighted mean Weighted mean is calculated when certain values in a data set are more important than the others. For example, When weighted mean is used to represent the average duration of stay by a patient in a hospital, the total number of cases presenting to each ward is taken as the weight.

## Measures of central tendency: The mean

Geometric Mean It is defined as the arithmetic mean of the values taken on a log scale. It is also expressed as the nth root of the product of an observation.

Open in a separate window GM is an appropriate measure when values change exponentially and in case of skewed distribution that can be made symmetrical by a log transformation. GM is more commonly used in microbiological and serological research.

One important disadvantage of GM is that it cannot be used if any of the values are zero or negative. The median cannot be identified for categorical nominal data, as it cannot be logically ordered. What is the mean?

The mean is the sum of the value of each observation in a dataset divided by the number of observations. This is also known as the arithmetic average. Looking at the retirement age distribution again: Advantage of the mean: The mean can be used for both continuous and discrete numeric data.

Limitations of the mean: The mean cannot be calculated for categorical data, as the values cannot be summed. As the mean includes every value in the distribution the mean is influenced by outliers and skewed distributions. What else do I need to know about the mean?

### Measures of central tendency: Median and mode

How does the shape of a distribution influence the Measures of Central Tendency? When a distribution is symmetrical, the mode, median and mean are all in the middle of the distribution. The following graph shows a larger retirement age dataset with a distribution which is symmetrical.

Mean Median and Mode: Understanding and Calculating Measures of Central Tendency

The mode, median and mean all equal 58 years. In a skewed distribution, the median is often a preferred measure of central tendency, as the mean is not usually in the middle of the distribution.

A distribution is said to be positively or right skewed when the tail on the right side of the distribution is longer than the left side.

Although there are exceptions to this rule, generally, most of the values, including the median value, tend to be less than the mean value. The following graph shows a larger retirement age data set with a distribution which is right skewed. The data has been grouped into classes, as the variable being measured retirement age is continuous.

## Australian Bureau of Statistics

The mode is 54 years, the modal class is years, the median is 56 years and the mean is A distribution is said to be negatively or left skewed when the tail on the left side of the distribution is longer than the right side. Although there are exceptions to this rule, generally, most of the values, including the median value, tend to be greater than the mean value.

The following graph shows a larger retirement age dataset with a distribution which left skewed. The mode is 65 years, the modal class is years, the median is 63 years and the mean is