Descriptive Statistics Test 31

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Descriptive Statistics Test 31

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Question 1
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Directions For Questions

Study the bar chart and answer the question based on it.

...view full instructions

In how many of the given years was the production of fertilizers more than the average production of the given years?

A
1

B
2

C
3

D
4

Solution

Average production (in 10000 tonnes) over the given years
$$= \dfrac{1}{8} (25 + 40 + 60 + 45 + 65 + 50 + 75 + 80) = 55$$.
$$\therefore$$ The productions during the years 1997, 1999, 2001 and 2002 are more than the average production.
Question 2
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Directions For Questions

The following chart shows the production of cars in thousands.

...view full instructions

For how many companies has there been no decrease in production in any year from the previous year?

A
One

B
Two

C
Three

D
Four

Solution

By visual inspection, we can say that Honda, GM, and Maruti have not shown a decrease.'
Question 3
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Directions For Questions

The following line graph gives the percentage of the number of candidates who qualified an examination out of the total number of candidates who appeared for the examination over a period of seven years from 1994 to 2000.

...view full instructions

In which pair of years was the number of candidates qualified, the same?

A
1995 and 1997

B
1995 and 2000

C
1998 and 1999

D
Data inadequate

Solution

The graph gives the data for the percentage of candidates qualified to appeared and unless the absolute values of number of candidates qualified or candidates appeared is know we cannot compare the absolute values for any two years.
Hence, the data is inadequate to solve this question.
Question 4
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Directions For Questions

Study the bar chart and answer the questions.

...view full instructions

The difference in the sales of cellular phones for the years $$1997$$ and $$1999$$ is?

A
$$500$$ units

B
$$1,000$$ units

C
$$5,000$$ units

D
$$18,000$$ units

Solution

The given graph shows the sale of cellular phones in the years $$1997, 1998, 1999, 2000,2001$$ and $$2002$$.

In the year $$1997$$, the sale of cellular phones is $$48000$$.
In the year $$1999$$, the sale of cellular phones is $$30000$$.

Therefore, the difference in the sales of cellular phones for the year $$1997$$ and $$1999$$ is,
$$48000-30000=18000$$

Hence, the difference in the sales of cellular phones for the year $$1997$$ and $$1999$$ is $$18,000$$ units.
Thus, option $$D$$ is correct.
Question 5
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Suppose a researcher is concerned with a nominal scale that identifies users versus nonusers of bank credit cards. The measure of central tendency appropriate to this scale is the

A
Mean

B
Mode

C
Median

D
Average

Solution

The mode is the value that appears most often in a set data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled. The mode of a continuous probability distribution is the value x at which its probability density function has its maximum value, so the mode is at the peak.
Option B is correct.
Question 6
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Directions For Questions

The bar graph given below shows the data of the production of paper (in lakh tonnes) by three different companies X, Y and Z over the years.

...view full instructions

The average production for five years was maximum for which company?

A
X

B
Y

C
Z

D
X and Z both

Solution

Average production (in lakh tons) in five years for the three companies are:
For Company X $$= \left [ \dfrac{1}{5} \times ( 30 +45 + 25 + 50 + 40) \right] = \dfrac{190}{5} = 38$$
For Company Y $$= \left [ \dfrac{1}{5} \times ( 25 +35 + 35 + 40 + 50) \right] = \dfrac{185}{5} = 37$$
For Company Z $$= \left [ \dfrac{1}{5} \times ( 35 +40 + 45 + 35 + 35) \right] = \dfrac{190}{5} = 38$$
$$\therefore$$ Average production of five years is maximum for both the Companies X and Z.
Question 7
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What was the percentage increase in imports from 1997 to 1998 ?

A
72

B
56

C
28

D
Data inadequate

Solution

The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.
Question 8
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The degree to which numerical data tend to spread about value is called

A
mean

B
variation

C
median

D
mode

Solution

Variance gives the degree to which the numerical data tend to spread about the value.

Variance is given by $$\dfrac{\sum x^2}{n}-(\dfrac{\sum x}{n})^2$$
Question 9
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All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $$10$$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given.

A
Median

B
Mode

C
Variance

D
Mean

Solution

The variance and standard deviation doesn't change even after addition of some constant to the given observations.
Question 10
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If $$x $$ is increased by $$k$$ then $$\sigma$$ changes to

A
$$k+\sigma$$

B
$$k\sigma$$

C
$$k\sqrt{\sigma}$$

D
remains unchanged

Solution

By the properties of standard deviation,
$$\sigma(x+k)=\sigma(x)$$
Therefore, by the addition of the constant, the standard deviation remains unchanged.