Measures of Dispersion Test

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Measures of Dispersion Test - 3

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Question 1
1 / -0

Absolute measures of dispersion are

A
Expressed in terms of original unit of series

B
Expressed in ratios or percentage, also known as coefficients of dispersion.

C
Both

D
None

Solution

These measures give us an idea about the amount of dispersion in a set of observations. They give the answers in the same units as the units of the original observations. When the observations are in kilograms, the absolute measure is also in kilograms.
Question 2
1 / -0

The main disadvantage of the standard deviation is

A
It is used in many other statistical techniques

B
It is difficult to calculate by hand

C
It is a sensitive measure of dispersion

D
It takes into account all the values in the data set

Solution

It is very hard for a person to calculate square root and even square of deviations. Formula of standard deviation is very hard to remember.
Question 3
1 / -0

The variance

A
Involves squaring deviation scores and then dividing them together

B
Cannot be calculated on continuous data

C
Should be adjusted when we want to generalize from a sample to a population

D
Produces small values in square units due to taking the square root of deviations

Solution

Since variance is a relative measures which is free from the units in which the values have been expressed, they can be compared even across different groups having different units of measurement.
Question 4
1 / -0

The inter quartile range

A
Can be calculated by subtracting the median from the fourth quartile

B
Relies on four values and therefore does not provide a measure of dispersion

C
Is representative of the middle 50% of values in the data set

D
Is normally used when the measure of central tendency is the mode

Solution

In descriptive statistics, the interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartile. IQR = Q₃ − Q₁
Question 5
1 / -0

A measure of relative dispersion is given by the:

A
Standard deviation

B
Co-efficient of variance

C
Quartile deviation

D
Variance

Solution

Relative measures of dispersion, are also known as coefficients of dispersion, are obtained as ratios or percentages. The coefficient of variation (CV) is the ratio of the standard deviation to the mean (average).
Question 6
1 / -0

The heights in cm of a group of first year biology students were recorded. The variance of these heights was subsequently calculated. The unit of measurement for this variance is:

A
cm²

B
cm

C
m

D
m²

Solution

As the variance is mean of sum of square deviation so unit will be in squared cm.
Question 7
1 / -0

The number of protozoa seen under 5 separate microscope slides were 3,4,5,6 and 7. The sum of squared deviations of observations from their sample mean is:

A
0

B
1000

C
100

D
10.0

Solution

sum of squared deviations of observations = ∑(x_i-μ)²

μ= ∑X_i/N = (3+4+5+6+7)/5= 25/5= 5

(x_i-μ)= -2, -1, 0, 1, 2

∑(x_i-μ)²= 4+1+0+1+4= 10
Question 8
1 / -0

What would happen to the variance of a data set if we added 5 to every observation?

A
Variance decrease by 10

B
Variance decrease by 5

C
Variance increased by 5

D
No Change

Solution

variance is unaffected due to change of origin.

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Re-Attempt Weekly Quiz Competition

Measures of Dispersion Test - 3

Result

Measures of Dispersion Test - 3

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SHARING IS CARING

Question 1

Expressed in terms of original unit of series

Expressed in ratios or percentage, also known as coefficients of dispersion.

Both

None

Solution

Question 2

It is used in many other statistical techniques

It is difficult to calculate by hand

It is a sensitive measure of dispersion

It takes into account all the values in the data set

Solution

Question 3

Involves squaring deviation scores and then dividing them together

Cannot be calculated on continuous data

Should be adjusted when we want to generalize from a sample to a population

Produces small values in square units due to taking the square root of deviations

Solution

Question 4

Can be calculated by subtracting the median from the fourth quartile

Relies on four values and therefore does not provide a measure of dispersion

Is representative of the middle 50% of values in the data set

Is normally used when the measure of central tendency is the mode

Solution

Question 5

Standard deviation

Co-efficient of variance

Quartile deviation

Variance

Solution

Question 6

cm2

cm

m

m2

Solution

Question 7

0

1000

100

10.0

Solution

Question 8

Variance decrease by 10

Variance decrease by 5

Variance increased by 5

No Change

Solution

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cm²

m²