Студопедия

Главная страница Случайная страница

КАТЕГОРИИ:

АвтомобилиАстрономияБиологияГеографияДом и садДругие языкиДругоеИнформатикаИсторияКультураЛитератураЛогикаМатематикаМедицинаМеталлургияМеханикаОбразованиеОхрана трудаПедагогикаПолитикаПравоПсихологияРелигияРиторикаСоциологияСпортСтроительствоТехнологияТуризмФизикаФилософияФинансыХимияЧерчениеЭкологияЭкономикаЭлектроника






Theoretical information






Random errors can take place during experimental measurement of some physical quantity. As a result of n experiments, the sequence of values x 1, x 2, … xn is obtained. Let’s find out the smallest value xmin and the largest value xmax and divide the range into k equal intervals. The width of each interval is determined as follows

.

Now it is possible to determine a number of measurements within every interval D n 1, D n 2…D nk and calculate the rate of reappearance of the measured values in each interval D n 1/ n, D n 2/ n, … D nk / n.

To find out the distribution of random values, we are to draw a diagram. The measured magnitude is put on the abscissa axis and the rate of reappearance within the corresponding interval is put on the ordinate axis. Such a diagram is termed a histogram (Fig. 5.2). As it is evident from the histogram, some values appear more often than others.

If the number of values approaches infinity and interval magnitude tends to zero, the upper sides of rectangles form continuous curve. This curve and its function are termed distribution curve and distribution function. In practice, normal distribution law is mostly applied. A typical curve of normal random distribution is shown in Fig. 5.3. Analytic expression of this distribution has been received by German mathematician Gauss. Depending on a standard deviation s, the distribution curve can vary (see Fig. 5.3.).

Distribution function has the peak value (absolute error is equal to zero) when the measured value is equal to the true one.


Поделиться с друзьями:

mylektsii.su - Мои Лекции - 2015-2024 год. (0.005 сек.)Все материалы представленные на сайте исключительно с целью ознакомления читателями и не преследуют коммерческих целей или нарушение авторских прав Пожаловаться на материал