A descriptive summary of a dataset through a single value that reflects the center of the data distribution Show
What is Central Tendency?Central tendency is a descriptive summary of a dataset through a single value that reflects the center of the data distribution. Along with the variability (dispersion) of a dataset, central tendency is a branch of descriptive statistics. The central tendency is one of the most quintessential concepts in statistics. Although it does not provide information regarding the individual values in the dataset, it delivers a comprehensive summary of the whole dataset.  Measures of Central TendencyGenerally, the central tendency of a dataset can be described using the following measures:
Even though the measures above are the most commonly used to define central tendency, there are some other measures, including, but not limited to, geometric mean, harmonic mean, midrange, and geometric median. The selection of a central tendency measure depends on the properties of a dataset. For instance, the mode is the only central tendency measure for categorical data, while a median works best with ordinal data. Although the mean is regarded as the best measure of central tendency for quantitative data, that is not always the case. For example, the mean may not work well with quantitative datasets that contain extremely large or extremely small values. The extreme values may distort the mean. Thus, you may consider other measures. The measures of central tendency can be found using a formula or definition. Also, they can be identified using a frequency distribution graph. Note that for datasets that follow a normal distribution, the mean, median, and mode are located on the same spot on the graph. Related ReadingsThank you for reading CFI’s guide on Central Tendency. To keep learning and advancing your career, the following resources will be helpful:
Let's look at some definitions that are necessary for understanding different measures of central tendency. What is central tendency ?A measure of central tendency attempts to describe a dataset through a singular value. This singular value is meant to represent the center point or typical value in a dataset. There are three measures of central tendency we need to know about, mean (also referred to as average), median and mode. MeanThe mean is the measure of central tendency that you should be most familiar with. The process to find the mean is to sum all the values of the data set, and then divide by the number of data points. Find the mean value of rainfall for the days listed below
Solution The mean is given by the sum of all the values divided by the number of values. The sum of values is 10 + 12 + 0 + 5 + 17 + 2 + 29 + 1 + 4 + 14 = 94, and there are 10 values, so the mean rainfall for the ten days is given as 9.4mm. MedianWhen we have a set of data that is able to be ordered in some way, we can find the median. The process to find the median is as follows: Step 1: Order the data, from smallest to largest. Step 2: If the number of data points is odd, the middle number is the median, meaning we take the value Step 3: If the number of data points is even, then we take the mean value of the middle two values. This means we take mean of the and value. Find the median of the following data. 12, 3, 4, 7, 19, 13, 4, 8, 81 Solution The first thing we need to do is order the data from smallest to largest, and this results in 3, 4, 4, 7, 8, 12, 13, 19, 81 As this has an odd number of data points, the median is the middle number of the ordered dataset, giving a median of 8. Given below are the heights of 30 children in a class (height given in cm). Find the median height. 168, 172, 151, 145, 181, 162, 174, 159, 149, 180, 164, 171, 150, 143, 189, 167, 176, 156, 144, 186, 166, 177, 153, 140, 184, 163, 178, 158, 149, 187. Solution First of all, we must order the data from smallest to largest. We get: 140, 143, 144, 145, 149, 149, 150, 151, 153, 156, 158, 159, 162, 163, 164, 166, 167, 168, 171, 172, 174, 176, 177, 178, 180, 181, 184, 186, 187, 189. As thirty is even, to find the median we find the mean of the fifteenth and sixteenth values. The fifteenth value is 164, and the sixteenth value is 166. The mean of these values is , meaning the median value is 165. ModeThe mode of a set of data is the most common value in the dataset. If there are two or more values which are most common, both of these values are the mode. Find the mode of the following data set. 1, 2, 3, 4, 4, 5, 6, 6, 6, 6, 7 Solution The mode here would be 6, as this appears four times, which makes it the most common value. Find the mode of the following numbers. 1, 2, 2, 3, 3, 3, 5, 7, 7, 7, 9, 11, 134 Solution Both 3 and 7 appear three times, making them both the most common value, meaning the mode is 3 and 7. Choosing suitable measures of central tendencyEach measure of central tendency has its own advantages and disadvantages. For the mean, the advantages are that it uses all of the data, and is, therefore, representative of all the data. However, there are disadvantages to using the mean. It is disproportionately influenced by extreme values, which can throw the mean. The mean also cannot be used if our data isn't numerical, and takes the most computation out of all our measures of central tendency. For the mode, the advantages are that we can find the mode of a set of data, be it numeric or otherwise. There is also limited computation, as we only need to tally the data, meaning if our data comes pre-tallied then this aids the mode. However, a downside is that the mode doesn't necessarily exist. In addition, we can have multiple modes, which doesn't help us describe a lot about the data set. As well as this, the mode doesn't take into account the full data set. Our final measure of central tendency is the median. The advantages are that the median isn't affected by any outliers or extreme values, and we have very little calculation to do. On the flip side, it does require us to order the set of data, which for large sets of data, is lengthy and time-consuming. It also doesn't take into account the full set of data, which means this could bring in weak results. Measures of Central Tendency - Key takeaways
Which of the central tendencies measures the most repeated value?The central tendency can be found using the formulas of mean, median or mode in most of the cases. As we know, mean is the average of a given data set, median is the middlemost data value and the mode represents the most frequently occurring data value in the set.
Which of the following measures of central tendency is known as the central position of a data set?In these situations, the median is generally considered to be the best representative of the central location of the data. The more skewed the distribution, the greater the difference between the median and mean, and the greater emphasis should be placed on using the median as opposed to the mean.
Which will be the best measure of central tendency for these data?Mean is the most frequently used measure of central tendency and generally considered the best measure of it. However, there are some situations where either median or mode are preferred. Median is the preferred measure of central tendency when: There are a few extreme scores in the distribution of the data.
Is the measure or value which appears most frequently in a set of data?The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.
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Which measure of central tendency refers to the most repeated value in a set of data?
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