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Descriptive Statistics Definition Descriptive statistics is a set of brief descriptive coefficients that summarize a given data set representative of an entire or sample population. How to Use the Winsorized Mean Winsorized mean is an averaging method that involves replacing the smallest and largest values of a data set with the observations closest to them. What Is a Bell Curve? A bell curve describes the shape of data conforming to a normal distribution.
What Is a Trimmed Mean? A trimmed mean is a method of averaging that removes a small percentage of the largest and smallest values before calculating the mean. Partner Links. Related Articles. Economy Median Income by State. So what's the middle number now that we've ordered it? We already knew that. And so there's actually going to be two middles.
If you have an even number, there's actually two numbers that qualify for close to the middle. And to actually get the median, we're going to average them. So 23 will be one of them. That, by itself, can't be the median because there's three less than it and there's four greater than it. And 25 by itself can't be the median because there's three larger than it and four less than it. So what we do is we take the mean of these two numbers and we pick that as the median.
So if you take 23 plus 25 divided by 2, that's 48 over 2, which is equal to So even though 24 isn't one of these numbers, the median is So this is the middle number. So once again, this is one way of thinking about central tendency.
If you wanted a number that could somehow represent the middle. And I want to be clear, there's no one way of doing it. This is one way of measuring the middle. Let me put that in quotes.
The middle. So, the median is There are 8 numbers in the set -- an even number. So, find the average of the middle two numbers, 10 and In this case, there are two modes -- 5 and 8 both occur twice, whereas the other numbers only occur once. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.
Consider this set of numbers: 5, 7, 9, 9, Since you have an odd number of scores, the median would be 9. You have five numbers, so you divide 5 by 2 to get 2. The number in the third position is the median. What happens when you have an even number of scores so there is no single middle score? Consider this set of numbers: 1, 2, 2, 4, 5, 7. Since there is an even number of scores, you need to take the average of the middle two scores, calculating their mean.
Remember, the mean is calculated by adding the scores together and then dividing by the number of scores you added.
Then, you take 6 and divide it by 2 the total number of scores you added together , which equals 3. So, for this example, the median is 3. Since the mode is the most frequently occurring score in a distribution, simply select the most common score as your mode. Consider the following number distribution of 2, 3, 6, 3, 7, 5, 1, 2, 3, 9.
The mode of these numbers would be 3 since three is the most frequently occurring number. In cases where you have a very large number of scores, creating a frequency distribution can be helpful in determining the mode. In some number sets, there may actually be two modes. This is known as bi-modal distribution and it occurs when there are two numbers that are tied in frequency. For example, consider the following set of numbers: 13, 17, 20, 20, 21, 23, 23, 26, 29, In this set, both 20 and 23 occur twice.
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