HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 574

Definitions The definitions used for these quantities are the following: Suppose that you have a number data points x1, x2, x3, ..., representing different measurements of the same discrete or continuous variable x. The set of all possible values of the quantity x is referred to as the population of x. A finite population will have only a fixed number of elements xi. If the quantity x represents the measurement of a continuous quantity, and since, in theory, such a quantity can take an infinite number of values, the population of x in this case is infinite. If you select a sub-set of a population, represented by the n data values {x1, x2, ..., xn}, we say you have selected a sample of values of x. Samples are characterized by a number of measures or statistics. There are measures of central tendency, such as the mean, median, and mode, and measures of spreading, such as the range, variance, and standard deviation. Measures of central tendency The mean (or arithmetic mean) of the sample, x, is defined as the average value of the sample elements, ∑ x = 1 n ⋅ n i =1 xi . The value labeled Total obtained above represents the summation of the values of x, or Σxi = n⋅x. This is the value provided by the calculator under the heading Mean. Other mean values used in certain applications are the geometric mean, xg, or the harmonic mean, xh, defined as: xg = n x1 ⋅ x2 L xn , ∑ 1 = n 1 . xh x i=1 i Examples of calculation of these measures, using lists, are available in Chapter 8. The median is the value that splits the data set in the middle when the elements are placed in increasing order. If you have an odd number, n, of ordered elements, the median of this sample is the value located in position Page 18-3