 # Measures Of Central Tendency And Variability Pdf

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Published: 18.04.2021  Obtaining descriptive statistics often involves using a few numbers to summarise data. There are two aspects involved in using descriptive statistics:.

In statistics , a central tendency or measure of central tendency is a central or typical value for a probability distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late s.

## Central tendency

Three such middle numbers are the mean, the median, and the mode. You could express your daily earnings from Table 1 in a number of ways. One way is to use the average, or mean, of the data set. The arithmetic mean is the sum of the measures in the set divided by the number of measures in the set. If there is an even number of items in a set, the median is the average of the two middle values. For example, if we had four values—4, 10, 12, and 26—the median would be the average of the two middle values, 10 and 12; in this case, 11 is the median.

In statistics, the range is a measure of the total spread of values in a quantitative dataset. Unlike other more popular measures of dispersion, the range actually measures total dispersion between the smallest and largest values rather than relative dispersion around a measure of central tendency. The range is interpreted as t he overall dispersion of values in a dataset or, more literally, as the difference between the largest and the smallest value in a dataset. The range is measured in the same units as the variable of reference and, thus, has a direct interpretation as such. This can be useful when comparing similar variables but of little use when comparing variables measured in different units.

Variability refers to how "spread out" a group of scores is. To see what we mean by spread out, consider graphs in Figure 1. These graphs represent the scores on two quizzes. The mean score for each quiz is 7. Despite the equality of means, you can see that the distributions are quite different. Specifically, the scores on Quiz 1 are more densely packed and those on Quiz 2 are more spread out. ## Central Tendency & Variability

Measures of central tendency: categories or scores that describe what is "average" or "typical" of a given distribution. These include the mode, median and mean. Percentile: a score below which a specific percentage of a given distribution falls. Positively skewed distribution: a distribution with a handful of extremely large values. Negatively skewed distribution: a distribution with a handful of extremely low values. Measures of variability: numbers that describe the diversity or dispersion in the distribution of a given variable. Box plot: a graphic representation of the range, interquartile range and median of a given variable.

Jump to navigation. Measures of Central Tendency provide a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution. There are three main measures of central tendency: the mean, the median and the mode. The mean of a data set is also known as the average value. It is calculated by dividing the sum of all values in a data set by the number of values. Disadvantages to the mean as a measure of central tendency are that it is highly susceptible to outliers observations which are markedly distant from the bulk of observations in a data set , and that it is not appropriate to use when the data is skewed, rather than being of a normal distribution. The median of a data set is the value that is at the middle of a data set arranged from smallest to largest. ## Central tendency

In any research, enormous data is collected and, to describe it meaningfully, one needs to summarise the same. The bulkiness of the data can be reduced by organising it into a frequency table or histogram. These measures may also help in the comparison of data. The mean, median and mode are the three commonly used measures of central tendency. Mean is the most commonly used measure of central tendency.

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