MCQ

MCQ 11 Mark

The coefficient of ___________ is a measure of the shape of a distribution.

A
Skewness
B
Kurtosis
✓
Both (a) and (b)
D
None

Answer

Correct option: C.

Both (a) and (b)

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MCQ 21 Mark

The degree of peakness or flatness of a unimodal distribution is called

A
Skewness
B
Symmetry
C
Dispersion
✓
Kurtosis

Answer

Correct option: D.

Kurtosis

(d) Kurtosis
Explanation : Kurtosis is a parameter that describe the peakness at centre and flatness at tails of a distribution.

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MCQ 31 Mark

In a symmetrical distribution the coefficien skewness will be :

✓
$0$
B
$Q_1$
C
$Q_3$
D
$1$

Answer

Correct option: A.

$0$

(a) 0
Explanation : For symmetrical distribution,
$
\text { Mean }=\text { Median }=\text { Mode }
$
So, in the case of symmetrical distribution, the coefficient of skewness will be zero.

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MCQ 41 Mark

Departure from symmetry is called

A
Second moment
B
Kurtosis
✓
Skewness
D
Variation

Answer

Correct option: C.

Skewness

(c) Skewness
Explanation : Here, departure from symmetry is used for lack of symmetry. When there is a lack of symmetric, it means skewness.

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MCQ 51 Mark

The standard deviation of some temperature data in ${ }^{\circ} C$ is 5 . If the data were converted into ${ }^{\circ} F$, then the variance would be

✓
81
B
57
C
36
D
25

Answer

Correct option: A.

(a) 81
Explanation : Given,
$\sigma_C=5$
$
\begin{array}{l}
\text { We know that, } \quad C=\frac{5}{9}(F-32) \\
\Rightarrow \quad F=\frac{9 C}{5}+32 \\
\therefore \quad \sigma_F=\frac{9}{5} \sigma_C=\frac{9}{5} \times 5=9 \\
\sigma_F^2=(9)^2=81 .
\end{array}
$

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MCQ 61 Mark

The following information relates to a sample of size $60, \Sigma x^2=18000, \Sigma x=960$. Then, the variance is

A
6.63
B
16
C
22
✓
44

Answer

Correct option: D.

(d) 44
Explanation : We know that,
$\operatorname{Variance}\left(\sigma^2\right)=\frac{\Sigma x_i^2}{N}-\left(\frac{\Sigma x_i}{N}\right)^2$
$\begin{array}{l}=\frac{18000}{60}-\left(\frac{960}{60}\right)^2 \\ =300-256 \\ =44 .\end{array}$

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MCQ 71 Mark

The standard deviations for first ten natural numbers is

A
5.5
B
3.87
C
2.97
✓
2.87

Answer

Correct option: D.

2.87

(d) 2.87
Explanation : We know that S.D. of first n natural numbers = $\sqrt{\frac{n^2-1}{12}}$
Here, n = 10
$\therefore$ S.D. $=\sqrt{\frac{(10)^2-1}{12}}=\sqrt{\frac{99}{12}}$
$=\sqrt{8.25}=2.87$

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MCQ 81 Mark

If $x_1, x_2, \ldots . . . . . x_n$ be $n$ observation and $\bar{x}$ be their arithmetic mean. Then, formula for the standard deviation is given by

A
$\Sigma\left(x_i-\bar{x}\right)^2$
B
$\frac{\Sigma\left(x_i-\bar{x}\right)^2}{n}$
✓
$\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n}}$
D
$\sqrt{\frac{\sum x_i^2}{n}+\bar{x}^2}$

Answer

Correct option: C.

$\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n}}$

(c) $\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n}}$
Explanation : The formula for S.D., $\sigma=\sqrt{\frac{\Sigma\left(x_i-\bar{x}\right)^2}{n}}$.

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MCQ 91 Mark

Mean deviation of $n$ observations $x_1, x_2, \ldots . . x_n$ from their mean $\bar{x}$ is

A
$\sum_{i=1}^n\left(x_i-\bar{x}\right)$
B
$\frac{1}{n} \sum_{i=1}^n\left|x_i-\bar{x}\right|$
C
$\sum_{i=1}^n\left(x_i-\bar{x}\right)^2$
D
$\frac{1}{n} \sum_{i=1}^n\left(x_i-\bar{x}\right)^2$

Answer

B. $\frac{1}{n} \sum_{i=1}^n\left|x_i-\bar{x}\right|$
Explanation : Mean Deviation, MD $=\frac{1}{n} \sum_{i=1}^n\left|x_i-\bar{x}\right|$
where, $\bar{x}$ is mean
$n$ is number of observations

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MCQ 101 Mark

The mean derivation of the data $3,10,10,4,7,10,5$ from the mean is

A
2
B
$2.57$
C
3
D
$3.75$

Answer

B. $2.57$
Explanation : Given observations are :
3,10,10,4,7,10,5
$\therefore \bar{x}=\frac{3+10+10+4+7+10+5}{7}=\frac{49}{7}=7$

$x_i$	$d_i=\left\|x_i-\bar{x}\right\|$
3 10 10	4 3 3
4 7 10 5	3 0 3 2
Total	$\Sigma d_i=18$

Mean Deviation $=\frac{\Sigma d i}{n}=\frac{18}{7}=2.57$.

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MCQ 111 Mark

Dispersion measures

A
The scatterness of a set of observations
B
The concentration of a set of observations
C
Both (a) and (b)
D
Neither (a) nor (b)

Answer

A. The scatterness of a set of observations
Explanation : The number that describes the variability or scatterness of a set of observations, is called measure of dispersion.

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MCQ 121 Mark

The appropriate measure of dispersion for open-end classification is

A
Standard deviation
B
Quartile Deviation
C
Mean deviation
D
All these measures

Answer

B. Quartile Deviation
Explanation : Quartile deviation provides the best measure of dispersion for open-end classification. It is also less affected due to sampling fluctuations.

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MCQ 131 Mark

The median is equivalent to …..

A
the fifth decile $\left(D_5\right)$
B
the middle quartile $\left(Q_2\right)$
C
the $50^{\text {th }}$ percentile $\left(P_{50}\right)$
✓
all of these

Answer

Correct option: D.

all of these

(D)the middle quartile $\left(Q_2\right)$
Explanation :
$\begin{aligned} \text { Median } & =50^{\text {th }} \text { percentile } P_{50} \\ & =\text { middle Quartile }\left(Q_2\right) \\ & =5^{\text {th }} \text { decile }\left(D_5\right)\end{aligned}$

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MCQ 141 Mark

Third Quartile is