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Measures of Dispersion Test - 25

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Measures of Dispersion Test - 25
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Weekly Quiz Competition
  • Question 1
    1 / -0
    If Mean deviation is 16 then the standard deviation of the data is____.
  • Question 2
    1 / -0
    What is the Relative counterpart of Standard Deviation ?
  • Question 3
    1 / -0
    The Gini Coefficient lies between ______.
  • Question 4
    1 / -0
    Variance of first $$20 $$ natural number is 
    Solution
    Variance of first $$n$$ natural numbers is $$\displaystyle =\dfrac{\sum(x_i)^2}{n}-(Mean)^2$$
    $$=\dfrac{1^2+2^2+3^2.....n^2}{n}-(\dfrac{n+1}{2})^2$$
    $$\sigma^2=\dfrac{n(n+1)(2n+1)}{6n}-\dfrac{(n+1)^2}{4}$$
    $$\boxed{\sigma^2=\dfrac{n^2-1}{12}}$$
    So variance of first $$20$$ natural number
    $$=\sigma^2=\dfrac{20^2-1}{12}=\dfrac{399}{12}=\dfrac{133}{4}$$ 
  • Question 5
    1 / -0
    _________ may be defined as the positive square root of arithmetic mean of the squares of all the deviations of the values from their arithmetic mean.
    Solution
    Standard deviation may be defined as the positive square root of arithmetic mean of the squares of all the deviations of the values from their arithmetic mean.
    It is most commonly and widely used measure of dispersion.
  • Question 6
    1 / -0
    According to _____, "The measure of the scatteredness of the mass of figures in a series about an average is called the measure of variation or dispersion".
  • Question 7
    1 / -0
    The roots of the equation (x-2)(x-3)(x+3) are _______.
  • Question 8
    1 / -0
    Value of each sample observation is decreased by $$25$$, the range of the sample observation will ____________.
  • Question 9
    1 / -0
    What will be the relative range, if the spread of items in a given distribution lies between $$100$$ and $$180$$kg?
  • Question 10
    1 / -0
    The mean of the following observation is $$10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23$$.
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