Descriptive Statistics Test 3

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Descriptive Statistics Test 3

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Weekly Quiz Competition

Question 1
1 / -0

Which one of the following statements is correct ?

A
Th Standard deviation for a given distribution is the square of the variance.

B
The standard deviation for a given distribution is the square root of the variance.

C
The standard deviation for a given distribution is equal to the variance.

D
The standard deviation for a given distribution is half of the variance.

Solution

We know $$Variance(\sigma^2)=\dfrac{\sum(x-\overline{x})^2}{n}$$
Where,
$$\sigma^2$$ is variance
$$\overline{x}$$ is mean
$$n$$ is number of observations.
Standard deviation $$(\sigma)=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n}}$$
$$\therefore$$ We can see, the standard deviation for a given distribution is the square root of the variance.
Question 2
1 / -0

The measure of dispersion is

A
M.D.

B
S.D.

C
Q.D.

D
All of these

Solution

Mean deviation, standard deviation as well as quartile deviation is the measure of dispersion.
Hence, all of these are measure of dispersion.
(It is well known fact)
Question 3
1 / -0

Marks scored by Rishi in an examination (out of $$100$$ marks) in different subjects are shown by the bar graph given below. The ratio of the highest marks to the lowest marks is

A
$$4:3$$

B
$$3:4$$

C
$$9:16$$

D
$$12:9$$

Solution

Highest marks $$= 80$$
Lowest marks $$=60$$

Ratio $$= \dfrac{80}{60} = \dfrac{4}{3}$$
Question 4
1 / -0

Quartile deviation for a frequency distribution is given by

A
$$Q=\cfrac { 1 }{ 4 } (Q_{ 2 }-{ Q }_{ 1 })$$

B
$$Q=\cfrac { 1 }{ 3 } (Q_{ 3 }-{ Q }_{ 1 })$$

C
$$Q=\cfrac { 1 }{ 2 } (Q_{ 3 }-{ Q }_{ 1 })$$

D
$$Q=(Q_{ 3 }-{ Q }_{ 1 })$$

Solution

It is fundamental concept that quartile deviation of any frequency distribution is given by,$$Q = \cfrac{1}{2}(Q_3-Q_1)$$
Question 5
1 / -0

Marks scored by Rishi in an examination (out of $$100$$ marks) in different subjects are shown by the bar graph given above. Percentage of marks obtained is around $$70$$ in which of the following subjects.

A
Maths

B
English

C
Biology

D
Computers

Solution

From the bar graph shown in the figure, it can be seen that the marks in English and Computer lie between the scale of 60 and 80.
However, the marks scored in Computer tend to appear $$70$$ from the bar-graph.
Thus the correct option is D.
Question 6
1 / -0

If 25% of the observations in a frequency distribution are less than $$20$$ and 25% are more than $$40$$, then the quartile deviation is

A
20

B
30

C
40

D
10

Solution

Here $$Q_1 = 20, Q_3 = 40$$
Hence quartile deviation of the given frequency distribution is $$=\cfrac{1}{2}(Q_3-Q_1)=10$$
Question 7
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Quartile deviation is :

A
$$\cfrac { 4 }{ 5 } \sigma $$

B
$$\cfrac { 3 }{ 2 } \sigma $$

C
$$\cfrac { 2 }{ 3} \sigma $$

D
$$\cfrac { 5 }{ 4 } \sigma $$

Solution

It is fundamental concept that for moderately skewed distribution $$Q.D = \cfrac{2}{3}\sigma$$
Question 8
1 / -0

The median of a symmetrical distribution, whose lower and upper quartiles are 60 and 80 respectively, is

A
60

B
80

C
70

D
None of these

Solution

Given, lower quartile $$=60$$ and upper quartile $$=80$$
$$\therefore$$ median $$=\frac{\mbox{
lower quartile
}+\mbox{
upper quartile
}}{2}=\dfrac{60+80}{2}=70$$
Question 9
1 / -0

The measure of dispersion is

A
Mean deviation

B
S.D.

C
quartile deviation

D
all of the above

Solution

Measures of dispersion include:
1)Sample standard deviation
2)Interquartile range (IQR) or Interdecile range
3)Range
4)Mean difference
5)Median absolute deviation (MAD)
6)Average absolute deviation (or simply called average deviation)
7)Distance standard deviation
Question 10
1 / -0

A graph drawn using vertical bars is called

A
bar graph

B
line graph

C
pictograph

D
pie graph

Solution

Bar graph represents the data using rectangular bars. The length of the rectangular bar is proportional to the values that they represent. The bars can be plotted vertically or horizontally.

The above graph is an example of a bar graph with vertical bars. The number of TV sets produced daily is represented by each rectangular bar. For example, 100 TV sets are produced on Friday.

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Descriptive Statistics Test 3

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Descriptive Statistics Test 3

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SHARING IS CARING

Question 1

Th Standard deviation for a given distribution is the square of the variance.

The standard deviation for a given distribution is the square root of the variance.

The standard deviation for a given distribution is equal to the variance.

The standard deviation for a given distribution is half of the variance.

Solution

Question 2

M.D.

S.D.

Q.D.

All of these

Solution

Question 3

$$4:3$$

$$3:4$$

$$9:16$$

$$12:9$$

Solution

Question 4

$$Q=\cfrac { 1 }{ 4 } (Q_{ 2 }-{ Q }_{ 1 })$$

$$Q=\cfrac { 1 }{ 3 } (Q_{ 3 }-{ Q }_{ 1 })$$

$$Q=\cfrac { 1 }{ 2 } (Q_{ 3 }-{ Q }_{ 1 })$$

$$Q=(Q_{ 3 }-{ Q }_{ 1 })$$

Solution

Question 5

Maths

English

Biology

Computers

Solution

Question 6

20

30

40

10

Solution

Question 7

$$\cfrac { 4 }{ 5 } \sigma $$

$$\cfrac { 3 }{ 2 } \sigma $$

$$\cfrac { 2 }{ 3} \sigma $$

$$\cfrac { 5 }{ 4 } \sigma $$

Solution

Question 8

60

80

70

None of these

Solution

Question 9

Mean deviation

S.D.

quartile deviation

all of the above

Solution

Question 10

bar graph

line graph

pictograph

pie graph

Solution

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