Introduction to Statistical Process Control. Muhammad Amir Aslam. Читать онлайн. Newlib. NEWLIB.NET

Автор: Muhammad Amir Aslam
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: Математика
Год издания: 0
isbn: 9781119528432
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      Example 1.2

      The weights of nine items selected from the assembly line are given as

      24.3, 24.9, 23.6, 25.1, 26.7, 22.0, 21.8, 23.4, and 20.8. Calculate median of the weights.

      Arranging the values in ascending order

      20.8, 21.8, 22.0, 23.4, 23.6, 24.3, 24.9, 25.1, and 26.7.

      In case of even number of observations, the median is defined as the mean of the two most middle values.

      Example 1.3

      The weights of 10 items selected from the assembly line are given as

      24.3, 24.9, 23.6, 25.1, 26.7, 22.0, 21.8, 23.4, 24.1, and 20.8. Calculate median of the weights.

      Arranging the values in ascending order

      20.8, 21.8, 22.0, 23.4, 23.6, 24.1, 24.3, 24.9, 25.1, and 26.7.

      The median for grouped may be defined as

      where l is the lower class boundary of the median class and c is the cumulative frequency.

      The family of median consists of partitioning of observations into different parts. As median is defined as the value that divides the data into 2 equal parts, the observations may be divided into 4, 10, or 100 equal parts. These measures are known as the quantiles. When data are divided into four parts, then it is called quartiles. Upper and lower quartiles or Q1 and Q3 may be defined as

      and

      The decile is defined as the value that divides the data into 10 equal parts.

      The other values of deciles can be calculated accordingly as the subscript is multiplied with the numerator. For example, the sixth decile may be calculated as

      The percentiles may be defined as the value that divides the data into 100 equal parts:

      The other values of percentiles can be calculated accordingly as the subscript is multiplied with the numerator. For example, the 70th percentile may be calculated as

      The formula for the grouped data can be constructed accordingly.

       iii) The Mode

      The mode is defined as the most repeated value in any data set. It is denoted by

. If there is no repetition in the data, then there will be no value of this measure. This is the single measurement whose results may be no value of mode, one value of mode, two values of the mode, or more values of mode in any data set.

      The mode for the grouped data may be calculated as

       iv) The Range

      The range is defined as the difference between the maximum value and the minimum value of the data set:

      or

      The range for the grouped data may be calculated as

       v) The Quartile Deviation

      The quartile deviation is defined as the half of the difference between the third and the first quartiles of the data set. The formula for the quartile deviation is defined as

      It is to be noted that all the measures of dispersion are positive.

      The coefficient of QD can be calculated as

       vi) The Mean Deviation

      The mean deviation is defined as the average of the deviations from the mean or median; the deviations are taken without algebraic sign. So the average deviation calculated from mean is known as the mean deviation from mean and is defined as

      And for the grouped data these measures can be defined as

      And the mean deviation from median and is defined as

      The coefficient of MD is defined as

      It