Measures of Central TendancyMeasures of Central Tendencyare ways of describing the central position of a frequency distribution for a group of data. You can describe this central position using the mean, median, or mode. Which you use will depend on how much and the type of data you collected. Show
The arithmetic mean is the most commonly used measure of central tendency. The mean is essentially a model of a data set for normally distributed (non-skewed) data. The mean has one main disadvantage: it is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. That’s why we determined the skew.
MedianModeMedian The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data. In order to calculate the median, suppose we have the data below:
We first need to rearrange that data into order of magnitude (smallest first):
Our median mark is the middle mark - in this case, 56 (highlighted in bold). It is the middle mark because there are 5 scores before it and 5 scores after it. This works fine when you have an odd number of scores, but what happens when you have an even number of scores? What if you had only 10 scores? Well, you simply have to take the middle two scores and average the result. So, if we look at the example below:
We again rearrange that data into order of magnitude (smallest first):
Only now we have to take the 5th and 6th score in our data set and average them to get a median of 55.5. Mode: The mode is the most frequent score in our data set. On a histogram it represents the highest bar in a bar chart or histogram. You can, therefore, sometimes consider the mode as being the most popular option. An example of a mode is presented below: Normally, the mode is used for categorical data where we wish to know which is the most common category, as illustrated below: We can see above that the most common form of transport, in this particular data set, is the bus. However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency, such as below: Is the middle score for a set of data arranged in order of magnitude?The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.
What is the middle score for a set of data?The median is the middle score in the set. To find the median, start by arranging all of the data points from smallest to largest. In an odd-numbered set, the median will be the number in the very middle of the list. In an even-numbered set, you will need to calculate the average of the two middle numbers.
What is the middle score for a set of data that has been arranged from highest to lowest or lowest to highest?The Median of a Data Set
The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.
What is the Middlemost score?The median is the middlemost number. In other words, it's the number that divides the distribution exactly in half such that half the cases are above the median, and half are below. It's also known as the 50th percentile, and it can be calculated for ordinal and interval/ratio variables.
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The middle score for a set of data that has been arranged in order of magnitude
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