Central tendency is a statistical measure; a single score to define the center of a distribution. It is also used to find the single score that is most typical or best represents the entire group. No single measure is always best for both purposes. There are three main types: Show
Here is a variety of videos to help you understand the concepts of these measures, finding the median using a histogram, and finding a missing value given the mean. There are properties that will change in the mean depending on how scores are modified. When every score has a number added to it, the mean also gets the same number added to it (ex. if the mean is 8 and every score within the distribution as a 3 added to is, the new mean will be 11). When all the numbers are multiplied by a something, the mean is also multiplied by that something (ex. if the mean is 2 and all the numbers in the distribution were multiplied by 3, the new mean would be 6). When only a few scores are greater or lower, the mean value follows with it but it needs to be recalculated. The following videos detail what happens to the mean and median when increasing the highest value, the impact that removing the lowest value has on the mean and median, and estimating means and medians when given a graph. Computing Central Tendency MeasuresComputing the mean: The mean is pretty straightforward. One should add up all the values and divide that sum by the number of values. For example, if I have a data set of 5 (2, 6, 3, 2, 2), I would add all the numbers up (15) and divide that by 5 to get a mean of 3. Computing the median: Calculating the median involves lining up all the scores from smallest to biggest. The middle one is the median. If there are an even amount of numbers, the average of the 2 middle numbers is considered the median. Remember that the purpose of a median is to divide the data in half. When working with a discrete frequency distribution, please refer to the first video below. When working with a grouped or continuous frequency distribution, there are extra steps. Please refer to the second video included below. Computing the mode: Mode is the most frequent number which comes up. Whatever shows up the most in your frequency table, that’s the mode. There may be more than one mode, so keep this in mind. Computing weighted means: Overall mean is the sum of all the scores of group one plus the sum of all the scores in group two. All of this is then divided by n1+n2. In some cases you’ll get something like “group 1 consists of 5 people with an average score of 10 and group 2 consists of 8 people with an average score of 7.” In this case you would multiply 5 and 10 and add that to 8 times 7. You would then divide that number by the total number of people to get the weighted mean. Here is a helpful video: Central Tendency and How they Relate to Distribution ShapeThe shape of a distribution can help you determine which measure of central tendency is greatest.
When to Use Each MeasureIn regards to the mean, no situation precludes it, but it shouldn’t be used when there are extreme scores, skewed distributions, undetermined values, open-ended distributions, ordinal scales, or nominal scales. With the median, it’s appropriate to use when there are extreme scores, skewed distributions, undetermined values, open-ended distributions, or ordinal scales. It is not to be used when there is a nominal scale. The mode is good to use with nominal scales, discrete variables, and in describing shape, but it shouldn’t be used with interval or ratio data, except to accompany the mean or median. This chapter was originally posted to the Math Support Center blog at the University of Baltimore on June 4, 2019. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. What will happen to the mean of every score is increased by 5?Adding, subtracting, multiplying, or dividing each score by a constant: When every score in a distribution is changed by the same constant, the mean will change by that constant. For example, if we add a constant of 5 to each score in a distribution, then the mean will increase by 5.
What causes the mean to increase?If we add a data point that's above the mean, or take away a data point that's below the mean, then the mean will increase. If take away a data point that's above the mean, or add a data point that's below the mean, the mean will decrease.
Will changing the value of a score change the mean?Clearly, the condition for the mean to be retained is that the new entry is equal to the entry that it replaces. This means that changing the value of one score always changes the mean.
What happens to mean if 3 is added to each data value?Answer: If you add a constant to every value, the mean and median increase by the same constant.
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