Why is range not a measure of central tendency

We've already seen some measures of central tendency , such as mean , median , and mode. Here, we'll see range. Think of the range of a function like its spread.

How big is the difference between the largest and smallest values real numbers in the data set? To calculate range, subtract the minimum value in the data set from the maximum value. So, that means maximum value - minimum value. That makes it much easier to find out what the highest number and lowest numbers are. Sets of data with bigger differences between their smallest and largest value have bigger ranges.

Sets of data with smaller differences between their smallest and largest value have smaller ranges. We are going to focus on range in this explanation, but you can also review explanations in mean , median , and mode. But sometimes only 1 or 2 of them are applicable to your data set, depending on the level of measurement of the variable.

To decide which measures of central tendency to use, you should also consider the distribution of your data set. For normally distributed data, all three measures of central tendency will give you the same answer so they can all be used.

In skewed distributions, the median is the best measure because it is unaffected by extreme outliers or non-symmetric distributions of scores. The mean and mode can vary in skewed distributions. The measures of central tendency you can use depends on the level of measurement of your data. The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average.

Have a language expert improve your writing. Check your paper for plagiarism in 10 minutes. Do the check. Generate your APA citations for free! APA Citation Generator. Mode : the most frequent value. Median : the middle number in an ordered data set. Mean : the sum of all values divided by the total number of values. Positively skewed distribution Negatively skewed distribution In this histogram, your distribution is skewed to the right, and the central tendency of your data set is on the lower end of possible scores.

What are measures of central tendency? The 3 most common measures of central tendency are the mean, median and mode. The mode is the most frequent value. The median is the middle number in an ordered data set. HM is used when we want to determine the average sample size of a number of groups, each of which has a different sample size.

If all the values in a data set are the same, then all the three means arithmetic mean, GM and HM will be identical. As the variability in the data increases, the difference among these means also increases. Arithmetic mean is always greater than the GM, which in turn is always greater than the HM.

The other measures of central tendency median and mode and the guidelines for selecting the appropriate measure of central tendency will be dealt with in the subsequent issue. Source of Support: Nil. Conflict of Interest: None declared. National Center for Biotechnology Information , U. Journal List J Pharmacol Pharmacother v. J Pharmacol Pharmacother.

Author information Copyright and License information Disclaimer. Assistant Editor, Journal of Pharmacology and Pharmacotherapeutics. E-mail: moc. This is an open-access article distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3. This article has been cited by other articles in PMC. MEAN Mean is the most commonly used measure of central tendency.

Table 1 Standard statistical notations. Open in a separate window. We can clearly see, however, that the mode is not representative of the data, which is mostly concentrated around the 20 to 30 value range. To use the mode to describe the central tendency of this data set would be misleading. We often test whether our data is normally distributed because this is a common assumption underlying many statistical tests. An example of a normally distributed set of data is presented below:.

When you have a normally distributed sample you can legitimately use both the mean or the median as your measure of central tendency. In fact, in any symmetrical distribution the mean, median and mode are equal. However, in this situation, the mean is widely preferred as the best measure of central tendency because it is the measure that includes all the values in the data set for its calculation, and any change in any of the scores will affect the value of the mean. This is not the case with the median or mode.

We find that the mean is being dragged in the direct of the skew. 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. A classic example of the above right-skewed distribution is income salary , where higher-earners provide a false representation of the typical income if expressed as a mean and not a median.

If dealing with a normal distribution, and tests of normality show that the data is non-normal, it is customary to use the median instead of the mean. However, this is more a rule of thumb than a strict guideline. Sometimes, researchers wish to report the mean of a skewed distribution if the median and mean are not appreciably different a subjective assessment , and if it allows easier comparisons to previous research to be made.

Please use the following summary table to know what the best measure of central tendency is with respect to the different types of variable. For answers to frequently asked questions about measures of central tendency, please go the next page.

Measures of Central Tendency Introduction A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. Mean Arithmetic The mean or average is the most popular and well known measure of central tendency.

When not to use the mean The mean has one main disadvantage: it is particularly susceptible to the influence of outliers. Median The median is the middle score for a set of data that has been arranged in order of magnitude.

In order to calculate the median, suppose we have the data below: 65 55 89 56 35 14 56 55 87 45 92 We first need to rearrange that data into order of magnitude smallest first : 14 35 45 55 55 56 56 65 87 89 92 Our median mark is the middle mark - in this case, 56 highlighted in bold.