Measures of dispersion play an important role in any data set. These measures go along with the measures of central tendency and show you the variability of your data. Measures of central tendency will show you the different ways you can group your data. The three basic things they can tell you are the median, mean, and range. Measures of dispersion go hand in hand with the measures of central tendency. Their important role in statistics has been reinforced by Wild and Pfannkuch According to them, our perception of the variability of the data is one of the basic components of statistical thinking.
The way we perceive the variability gives us information on the dispersion, or spread of the data, in terms of a mean or a median. A mean, or an average, is very common in statistics.
There are three important components in measures of dispersion that are related to random variability 2 :. They can also help you figure out if your data is far from its central tendency. This is very helpful when it comes to comparing distributions and understanding the risks of making certain decisions 1. To sum up, the greater the dispersion, the less representative your central tendency is. We have seen that a variable is nothing but a concept that can be measured, and its value may vary across the sample from case to case.
The dependent and independent variables are used to represent the concept of cause and effect. Central Tendency:. Central tendency represents the most typical value in a set of numbers. It is a way to summarize the data. So once we have our data, we want to describe it i. So our goal is to find the number that represents the rest of data or the point around which the data is clustered or distributed.
Once we know this number, we can use it to compare the different groups of data. The technique used to measure the central tendency depends on the level of measurement of the variable.
There are mainly three measures of central tendency — Mean, Median and Mode. Mean is only appropriate with interval and ratio level data, and is the only measure of central tendency that incorporates all of the scores in the dataset. It is calculated by summing up the values of all the data points and then dividing by the number of data points.
Median is the data point that divides our data into upper and lower halves. The median is appropriate for ordinal, interval, and ratio level variables, but not nominal variables. Mode is the category that has the maximum data points or the value that occurs most frequently. It is the only measure of central tendency that can be used with nominal variables, but can also be used with the ordinal, interval, and ratio variables.
Eg: If we categorize the data points and observe that the category A has 20, B has 23 and C has 32 data points, then the mode is category C. Dispersion is used to measure the variability in the data or to see how spread out the data is. It measures how much the scores in a distribution vary from the typical score. This is measured by dispersion. When dispersion is low, the central tendency is more accurate or more representative of the data as majority of the data points are near the typical value, thus resulting in low dispersion and vice versa.
Assume that we measured the incomes of a random sample of population in the year and again in the year Your Registration is Successful. Please login and proceed with profile update. Got it!! The email has already been used, in case you have forgotten the password click here. Your have entered an invalid email id or your email ID is not registered with us. Home Statistics Assignment Help.
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