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Question:
What is Continuous Random Variable?
Answer: Continuous Random Variable: A variable is called a continuous variable if it can take on any value-fractional or integral––
within a
given interval,
i.e. its domain is an interval with all possible values without gaps. For continuous variables values are obtained by
measuring process. A continuous variable represents measurement data such as the age of a person, the height of a plant, the
weight
of a commodity, the temperature at a place, etc.
Question:
Explain coefficient of skewness & its formula.
Answer: The 'Coefficient of Skewness' shows the tendency of the data set values to 'bunch' at one end of its distribution, with the v
alues at the
other
end being relatively dispersed. The mode is the measure indicating the value where most bunching happens. Skewness is
measured by working out the extent to which the mode departs from the mean. If the mode is towards the lower values in the da
ta
set, then the skewness is said to be positive; if it occurs towards the higher values, the skewness is negative. Sk = mean -
mode/ S.D.
An alternative formula for the coefficient of skewness is often used. (This is based on the knowledge that the difference between
the
mean and the mode is generally about three times the difference between the mean and the median): Sk = 3 (mean - median) / S.D.
Question:
What is Co-efficient of variation?
Answer: Co-efficient of variation: It is used to compare the variability a
nd to check the consistency of two or more series. It is most
commonly used relative measure of dispersion. Symbolically, the coefficient of variation, denoted by C.V., is given by C.V =
[Standard deviation / Arithmetic mean] × 100 It is used as a criterio
n of consistent performance; the smaller the coefficient of
variation, the more consistent is the performance It is also used as the criterion of variability; the larger the coefficient
of variation,
the more variability in the data.
Question:
What is empirical rule?
Answer: According to the empirical rule: a) Approximately 68% of the measurements will fall within 1 standard deviation of the mean,
i.e.
within the interval (`X – S,`X + S) b) Approximately 95% of the measurements will fall within 2 stand
ard deviations of the mean,
i.e. within the interval (`X –
2S,`X + 2S). c) Approximately 100% (practically all) of the measurements will fall within 3 standard
deviations of the mean, i.e. within the interval (`X – 3S,`X + 3S).
Question:
Explain Kurtosis.
Answer:
KURTOSIS: The term kurtosis was introduced by Karl Pearson. This word literally means ‘the amount of hump’, and is used to
represent the degree of PEAKEDNESS or flatness of a unimodal frequency curve. When the values of a variable are closely
bunched
round the mode in such a way that the peak of the curve becomes relatively high, we say that the curve is LEPTOKURTIC. On the
other hand, if the curve is flat-topped, we say that the curve is PLATYKURTIC: The normal curve is a curve which is neithe
r very
peaked nor very flat, and hence it is taken as a basis for comparison. The normal curve itself is called MESOKURTIC. Kurtosis
measures the shape of a distribution,how values are ranged around the mean. A normal distribution has a kurtosis of 3.
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