Q.Find the range of the following values: 13, 21, 25, 29 and 37. Or Define the Lorenz ratio. Under what condition is the value of this ratio zero, and when is it equal to one? (3+2)

Range = Largest value − Smallest value = 70 − 8 = 62.

The given values are: 24, 13, 49, 52, 70, 8.

Arranging them in order: 8, 13, 24, 49, 52, 70.

• Largest value (Maximum) = 70
• Smallest value (Minimum) = 8

Range = Maximum − Minimum = 70 − 8 = 62

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Range = Highest value - Lowest value of a series; this is the simplest measure of dispersion, distinct from variance (based on squared deviations from the mean) and the Lorenz ratio (a measure of income/wealth inequality).

Measures of dispersion describe how spread out the values in a data series are. The range is the most elementary of these: it is calculated simply as

Range = Largest value - Smallest value

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The statement is TRUE: the range depends only on the two extreme observations (the maximum and the minimum) of a series and takes no account of any of the remaining, intermediate values.

By definition, Range = Highest value - Lowest value. To compute it, we only need to identify which observation is the largest and which is the smallest in the entire series -- every other value, however many of them there are and whatever they are, plays no role whatsoever in the calculation. This is exactly why the range is considered a crude (though quick and easy) measure of dispersion: two very different series can have the same range if their highest and lowest values happen to match, even though the values in between are distributed very differently (e.g. tightly cluster …

Range = Highest value − Lowest value = 5 − 5 = 0.

Range is the simplest measure of dispersion, defined as the difference between the largest and smallest observations in a data series. If every value in the series equals 5, then the highest value is 5 and the lowest value is also 5, so Range = 5 − 5 = 0. A …

The difference between the highest and lowest value of a series is called the Range.

Range = Highest value (L) − Lowest value (S). It is the crudest but quickest measure of dispersion/variability in a data series, used widely for a rough first idea of spread (e.g. daily temper …

Range is, by definition, the gap between a data set's largest and smallest values.

Among measures of dispersion, range is defined as the difference between the highest (maximum) and the lowest (minimum) value in a given set of observations: Range = Maximum value - Minimum value. It is distinct from the Lorenz Ratio (used to study income/wealth inequality), variance (the average of squared deviations from t …

Standard deviation's floor is zero (identical observations); for the five given negative numbers, the range works out to 8.

Main blank. Standard deviation is calculated as the square root of the variance, and variance itself is the average of squared deviations from the mean - since a square can never be negative, variance (and hence standard deviation) can never be negative either. The smallest possible value standard deviation can take is zero, which occurs precisely when every single observation in the data set is exactly equal to the mean (i.e., all values are identical, with no dispersion at all).

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Both statements are true: range is exactly max minus min, and standard deviation is invariant to adding a constant to every value.

Main statement - Range

Range is the simplest measure of dispersion, defined precisely as the difference between the largest (maximum) and the smallest (minimum) value in a set of observations: Range = L - S. This is exactly what the statement says, so it is TRUE.

Or - Effect of adding a constant on standard deviation

If a constant (here, 10) is added to EVERY value of a variable, the entire distribution simply shifts by that constant - but the MEAN also shifts by exactly the same constant (10), so every individual observation's DEVIATION FROM THE MEAN (xi - mean) remains completely unchanged. Since standard deviation depends only on these deviations (specifically, the square root of their average squared value), it is unaffected by such a shift - this is known as the 'independence of standard deviation from a change of origin'. (Standard de …

The range of the given values is 202.

Given values: 228, 145, 315, 113, and 298.

Largest value (L) = 315

Smallest value (S) = 113 …