File previews. I always find it difficult for students to understand which average to use. This is a brief introduction to deciding the best fit with a card match activity. Thank you to other TES members who also share. Creative Commons "Sharealike". Reviews 4. OpenLearn works with other organisations by providing free courses and resources that support our mission of opening up educational opportunities to more people in more places.
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Create your free OpenLearn profile. Course content Course content. Everyday maths 2 Wales Start this free course now. Which measure would make his average score appear the highest? The mean. By choosing the average with the highest value, his average score appears higher than if he was to use the mode or median to represent the data. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.
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.
For example, consider the wages of staff at a factory below:. Staff 1 2 3 4 5 6 7 8 9 10 Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k. The mean is being skewed by the two large salaries. Therefore, in this situation, we would like to have a better measure of central tendency. As we will find out later, taking the median would be a better measure of central tendency in this situation. Another time when we usually prefer the median over the mean or mode is when our data is skewed i.
If we consider the normal distribution - as this is the most frequently assessed in statistics - when the data is perfectly normal, the mean, median and mode are identical. Moreover, they all represent the most typical value in the data set. However, as the data becomes skewed the mean loses its ability to provide the best central location for the data because the skewed data is dragging it away from the typical value.
However, the median best retains this position and is not as strongly influenced by the skewed values. This is explained in more detail in the skewed distribution section later in this guide. 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:. 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.
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