Measures of Dispersion Test

Result

Measures of Dispersion Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Semi inter-quartile deviation is given by the formula _______.

A
$$Q_3 - Q_1$$

B
$$\frac{Q_3 - Q_1}{8}$$

C
$$\frac{(Q_3 - Q_1)}{2}$$

D
$$\frac{(Q_3 - Q_1)}{4}$$

Solution

Semi inter-quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q₁ and the third quartile is denoted as Q₃ .

Semi inter-quartile deviation = (Q₃-Q₁) /2

                           = (29-17)/2

                             = 12/2

                             = 6
Question 2
1 / -0

The measure of the dispersion which ignores signs of the deviations from a central value is _______.

A
range

B
quartile deviation

C
standard deviation

D
mean deviation

Solution

Mean deviation is the arithmetic average of the deviations of the observed values from an average of the observed values. While calculating mean deviation, mod function is used which makes all the deviations positive. Therefore, it ignores the negative signs of the deviations.
Question 3
1 / -0

The co-efficient of quartile deviation from the following observations is
$$10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34$$

A
$$0.26$$

B
$$0.16$$

C
$$0.06$$

D
$$0.36$$

Solution

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q₁ and the third quartile is denoted as Q₃ .
The coefficient of quartile deviation is found by dividing the difference between the first quartile and the third quartile by the sum between the first quartile and the third quartile.

In the given series, 10, 15,17,18,20,22,25,28,29,32,34.
Q₁= 17 and Q₃=29
Coefficient of quartile deviation =(Q₃-Q₁)/ (Q₃+Q₁)
= (29-17)/ (29+17)

= 12/46 = 0.26
Question 4
1 / -0

If a constant value $$15$$ is subtracted from each observation of a set, the variance is ________.

A
reduced by $$15$$

B
reduced by $$225$$

C
unaltered

D
increased by $$225$$

Solution

Variance is the mean of the squares of the deviations from the mean. Therefore, if a constant value that is 15 is subtracted from each observations of the set, then the variance will not be altered as the effect of such a act will be managed at the time of calculating the deviations of the series.
Question 5
1 / -0

If each observation of set is divided by $$10$$, the S.D of the new observations is ______.

A
$$10$$ times of S.D of original obs.

B
$$\frac{1}{100}$$th

C
Not changed

D
$$\frac{1}{10}$$th

Solution

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. So the deviations are affected by division and multiplication. Therefore, if each observation of the set id divided by 10 then the whole standard deviation also becomes 1/10 th of the prior standard deviation.
Question 6
1 / -0

Which measure of dispersion is least affected by extreme values?

A
Range

B
Mean deviation

C
Standard deviation

D
Quartile deviation

Solution

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q₁ and the third quartile is denoted as Q₃ . Therefore, quartile deviation is not affected by the extreme values of the series.
Question 7
1 / -0

Sum of squares of the deviations is minimum when deviations are taken from ________.

A
mean

B
median

C
mode

D
zero

Solution

Mean deviation is the arithmetic average of the deviations of the observed values from an average of the observed values.
Mean deviation from the mean calculates the arithmetic average of the deviations of the observed values from mean of the observed values. Sum of the squares of the deviations is minimum when deviations are taken from mean as mean is the arithmetic average of the series and disperse the whole series into individual minimum value therefore the sum of their squares is minimum.
Question 8
1 / -0

Which measure of dispersion ensures highest degree of reliability?

A
Range

B
Mean deviation

C
Standard deviation

D
Quartile deviation

Solution

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. It is considered as the best and most commonly used measure of dispersion to ensure high degree of reliability as it is a measure of average of deviations from the average.
Question 9
1 / -0

Range of a set of values is $$60$$ and maximum value in the series is $$80$$. The minimum value of the series is _______.

A
$$140$$

B
$$20$$

C
$$70$$

D
None of the above

Solution

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion.

Range = 60

In the given series, H= 80 and L= x

Range => 80-x = 60
=> x = 80-60 = 20
Question 10
1 / -0

If $$Q_3 + Q_1 = 108, Q_3 - Q_1 = 74$$; then Q.D is _______.

A
$$33$$

B
$$3.7$$

C
$$37$$

D
$$0.68$$

Solution

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q₁ and the third quartile is denoted as Q₃ .

Quartile deviation = (Q₃-Q₁) /2

= 74/2

= 37

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Re-Attempt Weekly Quiz Competition

Measures of Dispersion Test - 32

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Measures of Dispersion Test - 32

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SHARING IS CARING

Question 1

$$Q_3 - Q_1$$

$$\frac{Q_3 - Q_1}{8}$$

$$\frac{(Q_3 - Q_1)}{2}$$

$$\frac{(Q_3 - Q_1)}{4}$$

Solution

Question 2

range

quartile deviation

standard deviation

mean deviation

Solution

Question 3

$$0.26$$

$$0.16$$

$$0.06$$

$$0.36$$

Solution

Question 4

reduced by $$15$$

reduced by $$225$$

unaltered

increased by $$225$$

Solution

Question 5

$$10$$ times of S.D of original obs.

$$\frac{1}{100}$$th

Not changed

$$\frac{1}{10}$$th

Solution

Question 6

Range

Mean deviation

Standard deviation

Quartile deviation

Solution

Question 7

mean

median

mode

zero

Solution

Question 8

Range

Mean deviation

Standard deviation

Quartile deviation

Solution

Question 9

$$140$$

$$20$$

$$70$$

None of the above

Solution

Question 10

$$33$$

$$3.7$$

$$37$$

$$0.68$$

Solution

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