How do you locate the center of your data?
Finding the central location in a data distribution is simple. If you are faced with distributions that represent different data conditions, you should look for the area where most of the common values fall. You will be able to locate that region even if the shape and type of data are different. The area where the most common values are located is known as the central location.
The central tendency cannot be relied on to provide a complete picture of the distribution of data. It only summarizes one aspect of distribution. You must consider another the variability around the central value, which is another aspect of distribution. Although this is a topic for another day, we must say that measures of variability describe how far away the data points tend to fall from the center. You should also note that distributions with the same central tendency like mean can be quite different.
The mean also called the arithmetic average is the measure of central tendency that most students are familiar with. To calculate the mean, all you have to do is add up all the values and divide them by the number of observations. When calculating mean, you incorporate all values in your data. This means that if you change any value, the mean will also change. However, you cannot always depend on the mean to help you locate the center of the data accurately.
If the distribution is skewed, the mean will miss the mark. You must be probably asking yourself, why is this so? Well, this happens because the outliers have a considerable impact on the mean. Also, the mean is pulled away from the center by extreme values in the extended tail. You should only use the mean as a measure of central tendency when you have symmetric distribution.
The median is simply the value in the middle. The value that splits your dataset in half is your median. Before you find the value in the middle, you should arrange your data from the smallest to the largest. The method of calculating the median will depend on if the dataset has an odd or even number of entries. When your values number is even, find two of the innermost values and calculate their average. The median is less affected by skewed data and outliers.
The mode is the value with the highest frequency in the dataset. If you are asked to find the mode in a bar chart, then you should choose the highest bar. There are scenarios where you might have a multimodal distribution. This happens when your dataset has multiple values that are occurring the most frequently. If you notice that there is not value repeating itself in your dataset, it means your data do not have a mode.
The mode should be used with categorical, discrete, and ordinal data. It is the only measure of the tendency that can be used with categorical data. Also, if you are working with raw continuous data, don't be surprised if you cannot locate the model. To identify the mode in continuous data, identify the maximum value on a probability distribution plot.
Which is the best measure of central tendency?
For the symmetrical distribution of continuous data, the mean, mode, and median are equal. However, statisticians usually opt for the mean because it incorporates all values in the calculation. When you are working with data with a skewed distribution, the median is your best measure of central tendency.
The mean and the mode are better measures of central tendency when you are working with ordinal data. Similarly, you should use the mode for categorical data. Remember, when you are caught in a dilemma of choosing between the mean and the median as the better measure of central tendency, you are also deciding on the type of statistical hypothesis tests that are suitable for your data.
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