Tag: measures of dispersion and skewness

Questions Related to measures of dispersion and skewness

The median of the following observations is
$10, 8, -9, -12, 15, 0, 23, -3, -2, 13, -24, 28, 35, 42$

  1. $4$

  2. $-2$

  3. $7$

  4. $-9.75$


Correct Option: A

When all the observations are same, the relation between A.M., G.M and H.M is _________.

  1. A.M. = G.M. = H.M.

  2. A.M. = G.M. > H.M.

  3. A.M. > G.M. > H.M.

  4. A.M. < G.M. < H.M.


Correct Option: A

Geometric mean of two observations can be calculated only if ________.

  1. both the observations are positive

  2. one of the two observations is zero

  3. one of them is negative

  4. both of them are zero


Correct Option: A

For further algebraic treatment geometric mean is _______.

  1. suitable

  2. not suitable

  3. sometime suitable

  4. none of the above


Correct Option: B

If modal value is not clear in a distribution, it can be ascertained by the method of ________.

  1. grouping

  2. guessing

  3. summarizing

  4. trial and error


Correct Option: A

For further algebraic treatment harmonic mean is ______.

  1. suitable

  2. not suitable

  3. sometime suitable

  4. none of the above


Correct Option: B

Mean deviation of $7,10,10,15,10,8,8,7,3,2,10$ through mean is

  1. $3.14$

  2. $8$

  3. $\dfrac {4}{5}$

  4. None of these


Correct Option: A
Explanation:

mean $=\dfrac{\sum {x _1}}{n}=\dfrac{90}{11}\approx 8.18$

derivation through mean = $|x _i-\bar x|$
& mean of it is $=\dfrac{\sum|{x _i-\bar x}|}{n}$
$=\dfrac{(1.18+1.82+1.82+6.82+8.18+0.18+0.18+1.18+5.18+6.18+1.82)}{11}$
$=\dfrac{34.54}{11}=3.14$