M.C.Q

MCQ 11 Mark

Let l be the lower class limit of a class-interval in a frequency distribution and m be the mid point of the class. Then, the upper class limit of the class is:

A
$\text{m}+\frac{\text{l+m}}{2}$
B
$\text{l}+\frac{\text{m+l}}{2}$
✓
$2\text{m}-1$
D
$\text{m}-2\text{l}$

Answer

Correct option: C.

$2\text{m}-1$

Given that, the lower class limit of a class-interval is $l$ and the mid-point of the class is m. Let $u$ be the upper class limit of the class-interval.
Therefore, we have
$\text{m}=\frac{\text{l+u}}{2}$
$\Rightarrow l + u = 2m$
$\Rightarrow u = 2m - l$
Thus the upper class limit of the class is $(2m - l)$.
Hence, the correct choice is $(c)$.

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MCQ 21 Mark

The number of times a particular item occurs in a given data is called its:

A
Variation.
✓
Frequency.
C
Cumulative frequency.
D
Class-size.

Answer

Correct option: B.

Frequency.

The number of times a particular item occurs in a given data is called the frequency of the item. Hence, the correct choice is $(b)$.

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MCQ 31 Mark

The following marks were obtained by the students in a test:
$81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62$
The range of the marks is:

A
$9$
B
$17$
C
$27$
✓
$33$

Answer

Correct option: D.

$33$

The marks obtained by the students are $81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79$ and $62$.
The highest and lowest marks are $95$ and $62$ respectively. Therefore, the range of marks is
$95 - 62$
$= 33$
Hence, the correct option is $(d)$.

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MCQ 41 Mark

The difference between the highest and lowest values of the observations is called:

A
Frequency.
B
Mean.
✓
Range.
D
Class-intervals.

Answer

Correct option: C.

Range.

The difference between the highest and lowest values of the observations is called the range.
Hence, the correct choice is $(c)$

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MCQ 51 Mark

The difference between the upper and the lower class limits is called:

A
Mid-points.
✓
Class size.
C
Frequency.
D
Mean.

Answer

Correct option: B.

Class size.

The difference between the upper and the lower class limits is called the class size.
Hence, the correct choice is $(b)$.

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MCQ 61 Mark

Tallys are usually marked in a bunch of:

A
$3$
✓
$4$
C
$5$
D
$6$

Answer

Correct option: B.

$4$

Tallies are usually marked in a bunch of $4$.
Hence, the correct option is $(b)$.

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MCQ 71 Mark

In a frequency distribution, the mid-value of a class is $15$ and the class intervals is $4$. The lower limit of the class is:

A
$10$
B
$12$
✓
$13$
D
$14$

Answer

Correct option: C.

$13$

Let $l$ and $m$ respectively be the lower and upper limits of the class. Then the mid-value of the class is $\frac{\text{l+m}}{2}$ and the class-size is $(m - l)$.
Therefore, we have two equations
$\frac{\text{l+m}}{2}=15$
$\Rightarrow l + m = 30,$
$m - l = 4$
Subtracting the second equation from the first equation, we have
$(l + m) - (m - l) = 30 - 4$
$\Rightarrow l + m - m + l = 26$
$\Rightarrow 2l = 26$
$\Rightarrow l = 13$
Hence, the lower limit of the class is $13$. Thus, the correct choice is $(c)$.

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MCQ 81 Mark

Tally marks are used to find:

A
Class intervals.
B
Range.
✓
Frequency.
D
Upper limits.

Answer

Correct option: C.

Frequency.

Tally marks are used to find the frequencies.
Hence, the correct choice is $(c)$.

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MCQ 91 Mark

In the class intervals $10-20, 20-30, 20$ is taken in:

A
The interval $10-20$.
✓
The interval $20-30$.
C
Both intervals $10-20, 20-30$.
D
None of the intervals.

Answer

Correct option: B.

The interval $20-30$.

The given class intervals are $10-20, 20-30$. In these class intervals the value $20$ is lies in the class interval $20-30$.
Hence, the correct choice is $(b)$.

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MCQ 101 Mark

The width of each of nine classes in a frequency distribution is $2.5$ and the lower class boundary of the lowest class $10.6$
. Then the upper class boundary of the highest class is:

A
$35.6$
✓
$33.1$
C
$30.6$
D
$28.1$

Answer

Correct option: B.

$33.1$

The number of classes is $9$ and the uniform class size is $2.5$. The lower limit of the lower class (first class) is $10.6$.
Therefore, the upper limit of the last class is
$10.6 + (9 \times 2.5)$
$= 10.6 + 22.5$
$= 33.1$
Hence, the correct choice is $(b)$.

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MCQ 111 Mark

The mid-value of a class interval is $42$. If the class size is $10$, then the upper and lower limits of the class are:

✓
$47$ and $37$
B
$37$ and $47$
C
$37.5$ and $47.5$
D
$47.5$ and $37.5$

Answer

Correct option: A.

$47$ and $37$

Let $l$ and $m$ respectively be the lower and upper limits of the class. Then the mid-value of the class is $\frac{\text{l+m}}{2}$ and the class-size is $(l - m)$.
Given that the mid-value of the class is $42$ and the class-size is $10$. Therefore, we have two equations
$\frac{\text{l+m}}{2}=42$
$\Rightarrow l + m = 84,$
$m - l = 10$
Adding the above two equations, we have
$(l + m) + (m - l) = 84 + 10$
$\Rightarrow l + m + m - l = 94$
$\Rightarrow 2m = 94$
$\Rightarrow l = 37$
Substituting the value of $m$ in the first equation, we have
$l + 47 = 84$
$\Rightarrow l = 84 - 47$
$\Rightarrow l = 37$
Hence, the upper and lower limits of the class are $47$ and $37$ respectively. Thus, the correct choice is $(a)$.

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