At statistical processing of results of researches of various sort the received values often are grouped in the sequence of intervals. For calculation of the generalizing characteristics of such sequences sometimes it is necessary to calculate the middle of an interval - "central to option". Methods of its calculation are rather simple, but have some features following both from the scale used for measurement, and from the nature of group (opened or the closed intervals).
Instruction
1. If the interval is the site of the continuous numerical sequence, then for finding of its middle use usual mathematical methods of calculation of arithmetic-mean value. Put the minimum value of an interval (began it) with maximum (termination) and halve result - it is one of ways of calculation of arithmetic-mean value. For example, this rule is applicable, when it comes to age intervals. Let's tell, the mark in 27 years as (21+33)/2=27 will be the middle of an age interval in the range from 21 year to 33 years.
2. It is sometimes more convenient to use other method of calculation of arithmetic-mean value between the top and lower borders of an interval. In this option at first determine range width - take away minimum from the maximum value. Then divide the received size in half and add result to the minimum value of range. For example, if the lower bound corresponds to value 47.15, and top - 79.13, then width of range will be 79.13-47.15=31.98. Then the middle of an interval will be 63.14 as 47.15+(31.98/2) = 47.15+15.99 = 63.14.
3. If the interval is not the site of the usual numerical sequence, then calculate its middle according to recurrence and dimension of the used measuring scale. For example, if it is about the historical period, then the middle of an interval will be a certain calendar date. So for an interval from January 1, 2012 to January 31, 2012 date will be on January 16, 2012 the middle.
4. Except the usual (closed) intervals the statistical methods of researches can operate also with "open". At such ranges one of borders is not defined. For example, the open interval can be set by a formulation "of 50 years and is more senior". The middle in this case is defined by method of analogies - if all other ranges of the considered sequence have identical width, then it is supposed, as this open interval has the same dimension. Otherwise you should define dynamics of change of width of the intervals previous opened and to remove its conditional width, proceeding from the received change trend.