Which of the following data sets has the minimum variance?

  • A
    $1, 2, 3, 4, 5$
  • B
    $1, 1, 2, 3, 6$
  • C
    $1, 1, 2, 3, 5$
  • D
    $1, 1, 2, 2, 5$

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The marks obtained by students $A$ and $B$ in $3$ examinations are given below:
| | Exam $1$ | Exam $2$ | Exam $3$ |
|---|---|---|---|
| Marks of $A$ | $30$ | $20$ | $40$ |
| Marks of $B$ | $70$ | $0$ | $5$ |
The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

The data is obtained in tabular form as follows:
$x_i$$60$$61$$62$$63$$64$$65$$66$$67$$68$
$f_i$$2$$1$$12$$29$$25$$12$$10$$4$$5$

Find the standard deviation of the given data. (in $.69$)

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Let $X_{1}, X_{2}, \ldots, X_{18}$ be eighteen observations such that $\sum_{i=1}^{18}(X_{i}-\alpha)=36$ and $\sum_{i=1}^{18}(X_{i}-\beta)^{2}=90$,where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is $1$,then the value of $|\alpha-\beta|$ is ...... .

In an experiment with $15$ observations on $x$,we have $\sum x^2 = 2830$ and $\sum x = 170$. One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. The corrected variance is:

The coefficient of variation of $9, 3, 11, 5, 7$ is

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