How to find the middle of the interval

At the statistical processing of research results of various kinds obtained values are often grouped into a sequence of intervals. For the calculation of generalized characteristics of such sequences sometimes it is necessary to calculate the mid interval - the "Central option". Methods of calculation is quite simple, but have some peculiarities, deriving from used to measure the scale and character of groups (open or closed intervals).

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Instruction

If the interval is a section of a continuous numeric sequence, to find its middle use regular mathematical methods of calculating arithmetic mean values. The minimum value of the interval (its beginning) fold with the maximum (end) and divide the result in half is one way to calculate arithmetic mean values. For example, this rule applies when talking about the age of the intervalH. for example, the middle of the age interval ranging from 21 years to 33 years, will mark 27 years since (21+33)/2=27.

Sometimes it is more convenient to use a different method of calculating the arithmetic mean value between the upper and lower boundaries of the interval. In this embodiment, first determine the width of the range - subtract the maximum from minimum. Then divide the resulting amount in half and add the result to the minimum value of the range. For example, if the lower bound corresponds to the value 47,15, and the top - of 79.13, the width of the range will be of 79.13-47,15=31,98. Then the middle interval is of 63.14, as 47,15+(31,98/2) = 47,15+15,99 = 63,14.

If the interval is not the usual plot of a numerical sequence, figure it the middle in accordance with the cyclical nature and dimensionality of the measurement scale used. For example, if we are talking about the historical period, the middle interval will be a specific calendar date. So for the interval from 1 January 2012 to 31 January 2012 will be the date the middle of January 16, 2012.

Besides the usual (closed) intervals statistical methods of research can operate, and "open". At those ranges, one of the limits is not defined. For example, an open interval can be defined by the phrase "50 years and older." The middle in this case is determined by the method of analogy - if all the other bands of this sequence have the same width, it is assumed that this open interval has the same dimension. Otherwise, you need to determine the dynamics of the width of the interval preceding the open, and to withdraw its conditional width, based on the trends.

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