Basic Statistics

  • Newton Interpolation Formula for Unequal Intervals

    When the values of the independent variable occur with unequal spacing the formula discussed earlier is no more applicable. In this situation another formula which is based on divided difference is used. Before presenting the formula let us first discuss about what are divided differences. Divided Differences: Let the values of the independent variable are […]

  • Examples of Newton Interpolation

    Example No 1: The following supply schedule gives the quantity supplied in hundreds of a product at prices in rupees: 80 90 100 110 120 25 30 42 50 68   Interpolate, what will be the quantity supplied of the product at a price Dollor 85. Solution: Constructing the difference table first. THE DIFFERENCE TABLE […]

  • Newton Interpolation Formula

    A number of different formulae were given by Newton, however, two of these formulae are more common. One of these formulae is used when the independent variable assumes values with equal interval while the other is applicable when the interval is not equal. The first formula is referred to as “Newton’s formula for equal interval”, […]

  • Examples of Lagrange Interpolation

    Example No 1: Interpolate the value of the function corresponding to , using Lagrange’s Interpolation formula from the following set of data: 2 3 5 8 12 10 15 25 40 60   Solution: Using formula of Lagrange Interpolation, we have Now simplify the brackets terms and write them in brackets with their proper sign […]

  • Lagrange Interpolation Formula

    Lagrange’s formula is applicable to problems where the independence variable occur with equal and unequal intervals, but preferably this formula is applied in a situation where there are unequal intervals in the given independence series. Let the values of the independence variables are given as   etc., and the corresponding values of the function (dependent variable) […]

  • Introduction to Interpolation

    The time series data which is recorded after regular or irregular interval of time consists of values of a phenomenon at a certain point in time or the values of some hypothetical function corresponding to a few values of independent variable are not sufficient to provide information regarding the values of the same phenomenon in […]

  • Mathematical Curve Fitting

    Mathematical curve fitting is probably the most objective method of isolating trend. This method enables us to obtain precise estimates of the trend values based on some objective criterion. One of the major problems in using this method is the selection of an appropriate type of curve which best fit to the given data. However, […]

  • Isolation of Cyclical Movements

    The long term cyclical movements in a time series can be studied more or less in the same way as the seasonal movements. The data for the study of cyclical movements consists of large number of yearly observations and seasonal variations are assumed to be absent. The multiplicative model, as indicated earlier, is used to […]

  • Seasonal Component Additive Model

    Using the additive model i.e. , the de-trended series may be obtained by subtracting the trend values from the actual observations i.e., The remainder now consists of the seasonal and the residual components. The trend values that are subtracted might have been obtained by any of the methods described earlier, however, the moving trend or […]

  • Seasonal Component Multiplicative Model

    Using the multiplicative model i.e., the ratio detrended series may be obtained by dividing the actual observations by the corresponding trend values i.e., The remainder now consists of the seasonal and the residual components. The seasonal component may be isolated from the ratio-detrended series by averaging the detrended ratios for each month or quarter. The […]

  • Merits and Demerits of Moving Average Method

    Merits: Moving averages can be used for measuring the trend of any series. The method is applicable for linear as well as non-linear trends. Demerits: The trend obtained by moving averages is, in general, neither a straight line nor some standard curve. For this reason the trend cannot be extended for forecasting the future values. […]

  • Method of Moving Averages

    Suppose that there are times periods denoted by and the corresponding values of variable are . First of all we have to decide the period of the moving averages.  For short time series, we use period of 3 or 4 values. For long time series, the period may be 7, 10 or more. For quarterly […]