Give a brief note of measures of central tendency together with their merit & demerit which is the best measure of central tendency and why
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In addition, be sure to clarify your terms. Exactly what is meant by "central tendency"??
Measures of central tendency are statistical measures used to describe the center or typical value of a data set. The three main measures of central tendency are the mean, median, and mode. Here's a brief explanation of each measure and their merits and demerits:
1. Mean: The mean is calculated by summing up all the values in the data set and dividing it by the number of observations. It is the most commonly used measure of central tendency. Its merits include being sensitive to every value in the dataset, providing a representative value for the data, and being suitable for data that is normally distributed. However, the mean is influenced by outliers or extreme values and may not accurately represent skewed data sets.
2. Median: The median is the middle value in a sorted data set or the average of the two middle values for an even-numbered data set. It is not affected by extreme values and is a robust measure of central tendency. It is useful when dealing with skewed data or data with outliers. However, the median does not consider all values in the data set and may not provide an accurate representation of the entire data set.
3. Mode: The mode is the most frequently occurring value in a data set. It is useful for categorical or nominal data and can be applied to continuous data as well. The mode can handle bimodal or multi-modal data sets, and it is not influenced by extreme values. However, the mode may not exist (when there is no repeated value) or it can have multiple modes in some cases.
The choice of the best measure of central tendency depends on the nature and characteristics of the data set. There is no single best measure for all situations. The mean is commonly used for symmetric normal distribution data, while the median is preferred for skewed data or data with outliers. The mode is useful for categorical data or when identifying the most frequent value. It is essential to consider the distribution and characteristics of the data set when determining which measure of central tendency to use.