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Importance of measures of central tendency?
Measures of the general value are a common need. Average, Median, and Mode are the three commonest.Average is the arithmetic average of all the values.Median is the actual measurement which is midwaybetween the extreme values, and is often closest to the average.Mode is the commonest value.Other indicators of central tendency, may ignore all value beyond say, three standard deviations, and thus ignore the contribution by the extreme, and uncommon, values.
To determine the types of equipment your boat must carry you need to make a measurement. What is the measurement?
The length of the boat.
Why do you need the mean in maths?
The mean is one of the measures of central tendency. The other standard ones are the median and the mode. They each have their strengths and weaknesses. For the mean, also called the average, the idea of central tendency is this: every number that has gone into calculating the average has the same unweighted effect on the final average. Of course, the numbers that are out at the extremes can seem to have more pull, but you don't actually do anything different with those numbers. They are all treated exactly the same. You add all the data points together, and then divide that sum by the number of data points. So the mean represents equally each of the data points used in its calculation.This is a very important idea in statistics, where you figure out how to use measures of central tendency and other measures to say some surprisingly powerful things about the data you collect.
How do you figure out the perimeter of an triangle when you only have a measurement for the hypotenuse?
It is impossible. You need another measurement, such as angle, side length or area etc.
Why do you suppose there is not just one system of measurement?
Because the need for measurement is universal and it developed in different ways in primitive cultures. It is only later, with interregional, and then international trade that there was a need for a single system.
