Standard Deviation

Introduction

Standard deviation is the square root of arithmetic average of the squares of the deviations measured from mean. It was introduced by Karl Pearson in 1823. The relative measure of standard deviation is measured as the ratio of standard deviation with mean. It is also termed coefficient of standard deviation. When coefficient of standard deviation is multiplied by 100, it is termed as coefficient of variation. Coefficient of variation is a measure used to compare two or more series having different mean or having observations in different units of measurement. Standard deviation can be calculated in three types of series individual series, discrete series and continuous series.

The standard deviation for individual and continuous series can be calculated by three methods, namely actual mean or direct method, assumed mean or indirect method and step deviation method.

The properties of ideal measures of dispersion are easy to calculate and simple to understand, based on all the terms of a series, rigidly defined, capable of further algebraic treatment, etc.

The various merits of standard deviation are it is rigidly defined and therefore is dependable; it has all good qualities of arithmetic mean, etc.

The demerits of standard deviation are: as compared to range and quartile deviation, it is difficult to understand and compute, etc.

Lorenz curve is a graphical method of measuring dispersion based on cumulative information to indicate the degree of variability. It helps in studying variability in the distribution of income, profits and wealth.

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  • Q1

    Standard deviation is independent of origin but not of _________

    Marks:1
    Answer:

    scale.

    Explanation:

    If the values or deviations are divided by a common factor, the value of the common factor is used in the formula to get the value of the standard deviation.

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  • Q2

    The curve that lies below the line of equal distribution line is called ____________

    Marks:1
    Answer:

    Lorenz curve.

    Explanation:

    The Lorenz curve always lies below the line of equal distribution line, unless the distribution is uniform. If the distribution is uniform, the Lorenz curve will coincide with the line of equal distribution. The more Lorenz curve is away from the line of equal distribution, the greater the dispersion.

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  • Q3

    A measure least affected by the fluctuations of sampling is ___________

    Marks:1
    Answer:

    quartile deviation.

    Explanation:

    Standard deviation is rigidly defined and its value is always definite and based on all observations.

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  • Q4

    The concept of Standard Deviation was introduced by Karl Pearsons in

    Marks:1
    Answer:

    1893.

    Explanation:

    Standard deviation is not affected by the value of constant from which deviations are calculated. The value of the constant does not figure in the standard deviation formula.

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  • Q5

    The best measure of dispersion is

    Marks:1
    Answer:

    Standard deviation.

    Explanation:

    Standard deviation is the best and widely used measure of dispersion. The properties of standard deviation are:

    i)    Standard deviation is rigidly defined.

    ii)   It requires harder calculations.

    iii) It depends on all the values of the variable.

    iv) It is based on deviations from the arithmetic mean.

          v) It is capable of further statistical treatment.
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