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They may be used-with considerable caution-when the measurements in the various populations being compared were made in different units. Dividing the dispersion estimates by the location estimates eliminates eliminates the differences attributable to differences in measuring units. However, caution is advised because the measurement methods may have differed in the various populations, giving rise to differences in the dispersion estimates having nothing to do with dispersion in the populations. In other words, there could well be differing levels of measurement error across populations.
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3 Give a brief note of the measures of central tendency together with their merits and Demerits Which is the best measure of central tendency and why?
ANS: Measures of central tendency will quantify the middle of the distribution. The measures in case of population are the parameters and in case of sample, the measures are statistics that are estimates of population parameters. The three most common ways of measuring the centre of distribution is the mean, mode and median.In case of population, the measures of dispersion are used to quantify the spread of the distribution. Range, interquartile range, mean absolute deviation and standard deviation are four measures to calculate the dispersion.The measures of central tendency and measures of dispersion summarise mass data in terms of its two important features.i. With respect to nature of data to cluster around a central valueii. With respect to their spread from their central valueArithmetic mean is defined as the sum of all values divided by number of values.Median of a set of values is the middle most value when the values are arranged in the ascending order of magnitude.Mode is the value which has the highest frequencyThe measures of variations are:i. Range (R)ii. Quartile Deviations ( Q.D)iii. Mean Deviations (M.D)iv. Standard Deviations (S.D)Coefficient of variation is a relative measure expressed in percentage and is defined as:CV in %=
Is sigma square equal to variance?
Yes, sigma squared (σ²) represents the variance of a population in statistics. Variance measures the dispersion of a set of values around their mean, and it is calculated as the average of the squared differences from the mean. In summary, σ² is simply the symbol used to denote variance in statistical formulas.
What measures English measurements?
First: there is no such thing as English measurement.Second: Imperial measures are used for measuring things; nothing measures them!
What part of a graph or chart is used to compare relative parts of a whole?
A pier chart is used to compare relative parts of a whole.
What is absolute error formula?
Absolute and Relative Error Absolute and relative error are two types of error with which every experimental scientist should be familiar. The differences are important. Absolute Error: Absolute error is the amount of physical error in a measurement, period. Let's say a meter stick is used to measure a given distance. The error is rather hastily made, but it is good to ±1mm. This is the absolute error of the measurement. That is, absolute error = ±1mm (0.001m). In terms common to Error Propagation absolute error = Δx where x is any variable. Relative Error: Relative error gives an indication of how good a measurement is relative to the size of the thing being measured. Let's say that two students measure two objects with a meter stick. One student measures the height of a room and gets a value of 3.215 meters ±1mm (0.001m). Another student measures the height of a small cylinder and measures 0.075 meters ±1mm (0.001m). Clearly, the overall accuracy of the ceiling height is much better than that of the 7.5 cm cylinder. The comparative accuracy of these measurements can be determined by looking at their relative errors. relative error = absolute error value of thing measured or in terms common to Error Propagation relative error = Δx x where x is any variable. Now, in our example, relative errorceiling height = 0.001m 3.125m •100 = 0.0003% relativeerrorcylinder height = 0.001m 0.075m •100 = 0.01% Clearly, the relative error in the ceiling height is considerably smaller than the relative error in the cylinder height even though the amount of absolute error is the same in each case.
