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This math video tutorial gives a step by step explanation to a math problem on "Finding The Average Speed".

An average is a single value that is meant to typify a list of values. If all the numbers in the list are the same, then this number should be used. If the numbers are not all the same, an easy way to get a representative value from a list is to randomly pick any number from the list. However, the word 'average' is usually reserved for more sophisticated methods that are generally found to be more useful.

The most common type of average is the arithmetic mean, often simply called the mean. The arithmetic mean of two numbers, such as 2 and 8, is obtained by finding a value A such that 2 + 8 = A + A. It is then simple to find that A = (2 + 8)/2 = 5. Switching the order of 2 and 8 to read 8 and 2 does not change the resulting value obtained for A. The mean 5 is not less than the minimum 2 nor greater than the maximum 8. If we increase the number of terms in the list for which we want an average, we get, for example, that the arithmetic mean of 2, 8, and 11 is found by solving for the value of A in the equation 2 + 8 + 11 = A + A + A. It is simple to find that A = (2 + 8 + 11)/3 = 7.

Again, changing the order of the three members of the list does not change the result: A = (8 + 11 + 2)/3 = 7, and that 7 is between 2 and 11. This summation method is easily generalized for lists with any number of elements. However, the mean of a list of integers is not necessarily an integer. "The average family has 1.7 children" is a jarring way of making a statement that is more appropriately expressed by "the average number of children in the collection of families examined is 1.7".

Distance is a numerical description of how far apart objects are.

Speed is the rate of motion, or equivalently the rate of change in position, often expressed as distance d traveled per unit of time t.

Speed is a scalar quantity with dimensions distance/time; the equivalent vector quantity to speed is known as velocity. Speed is measured in the same physical units of measurement as velocity, but does not contain the element of direction that velocity has. Speed is thus the magnitude component of velocity.

In mathematical notation, it is simply: v = d / t

where v:speed, d:distance, and t:time.

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