Descriptive Statistics Test 30

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Descriptive Statistics Test 30

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Weekly Quiz Competition

Question 1
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Directions For Questions

Directions. (Ques 11-15) The students lend books from their school Library. The pictograph shows the number of books checked out in six days. Use the information from the graph to answer the questions. (Assume $$1$$ book $$= 15$$ books)

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How many fewer books were checked out on Saturday than Tuesday?

A
$$15$$

B
$$30$$

C
$$45$$

D
$$10$$

Solution

Tuesday $$= 5$$
Saturday $$= 3$$
So, the difference is $$5 - 3 = 2 \times 15 = 30$$ books were checked out on Tuesday than Saturday.
Question 2
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Directions For Questions

Amit, Bala, Frank, Madesh, Thomas are officers. The pictograph shows the earnings of five officers in a month. Use the information from the graph to answer the questions.

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How much less money did Thomas earn than Bala?

A
$$1800$$

B
$$900$$

C
$$1000$$

D
$$1200$$

Solution

Thomas earnings $$= 2 \times 450 = 900$$
Bala earnings $$= 4 \times 450 = 1800$$
So, the difference $$= 1800 - 900$$
$$= 900$$
Question 3
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According to the graph above, in which year was the ratio of the number of students enrolled at School $$B$$ to the number of students enrolled at School $$A$$ the greatest?

A
$$1990$$

B
$$1991$$

C
$$1992$$

D
$$1993$$

E
$$1994$$

Solution

As per given graph:
In year $$1990$$ number of students enrolled at school $$B$$ is $$1200$$ and school $$A$$ is $$800$$
Then ratio of $$B$$ to $$A$$ $$=$$ $$\dfrac{1200}{800}=\dfrac{3}{2}$$
In year $$1991$$ number of students enrolled at school $$B$$ is $$800$$ and school $$A$$ is $$1600$$
Then ratio of $$B$$ to $$A$$ $$=$$ $$\dfrac{800}{1600}=\dfrac{1}{2}$$
In year $$1992$$ number of students enrolled at school $$B$$ is $$2000$$ and school $$A$$ is $$1200 $$
Then ratio of $$B$$ to $$A$$ $$=$$ $$\dfrac{2000}{1200}=\dfrac{5}{3}$$
In year $$1993$$ number of students enrolled at school $$B$$ is $$1600$$ and school $$A$$ is $$1600 $$
Then ratio of $$B$$ to $$A$$ $$=$$ $$\dfrac{1600}{1600}=\dfrac{1}{1}$$
In year $$1994$$ number of students enrolled at school $$B$$ is $$1600$$ and school $$A$$ is $$800 $$
Then ratio of $$B$$ to $$A$$ $$=$$ $$\dfrac{1600}{800}=\dfrac{2}{1}$$
Then in year $$1994$$ the ratio is greatest
So, answer is $$(E)$$, $$1994$$ is correct.
Question 4
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Which year did the same number of boys and girls attend the conference?

A
1995

B
1996

C
1997

D
1998

E
None
Question 5
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The mean of a finite set X of numbers is $$14$$, the median of this set of numbers is $$12$$, and the standard deviation is $$1.8$$. A new set Y is formed by multiplying each member of the set S by $$3$$. Determine the correct statements w.r.t. set Y:
I. The mean of the numbers is set Y is $$42$$
II. The median of the numbers in set Y is $$36$$
III. The standard deviation of the numbers is set Y is $$5.4$$

A
I only

B
II only

C
I and II only

D
I and III only

E
I, II, and III

Solution

For set $$x$$
Mean $$=14$$
Median$$=12$$
S.D.$$=\sqrt { \sigma } $$
$$=1.8$$.

For set $$y$$
Mean $$=14\times 3= 42$$.
Median $$=12\times 3=36$$.
SD$$=1.8\times 3= 5.4$$.

Hence all three are correct.
Question 6
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How many watches were sold in all 5 months?

A
160

B
180

C
175

D
170

Solution

Total Sales= Addition of sales individually in each month.
Total Sale$$=20+50+20+60+30=180$$
Question 7
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Grades for the test on proofs did not go as well as the teacher had hoped. The mean grade was 68, the median grade was 64, and the standard deviation was 12. The teacher curves the score by raising each score by a total of 7 points. Which of the following statements is true?
I. The new mean is 75.
II. The new median is 71.
III. The new standard deviation is 7.

A
I only

B
III only

C
I and II only

D
I, II, and III

E
None of the statements are true

Solution

If each observation is increased by $$7$$ then the mean will also be increased by $$7$$.
New Mean = Old Mean $$+7=68+7=75$$

If each observation is increased by $$7$$ then the median will also be increased by $$7$$.
New median = Old median$$+7=64+7=71$$

If each observation is increased/decreased by any quantity the standard deviation will remain same.
New standard deviation= old standard deviation $$=12$$
Question 8
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The figure above shows the cost of joining and buying music from a music subscription service. What does the y-intercept of the line most likely represent?

A
The cost per song

B
The cost to join the service

C
The cost of buying 20 songs

D
The cost of 20 subscriptions to the service

Solution

When no. of songs are 0 then cost is 20$. This means the cost of joining the service is 20$.
Hence, the y-intercept (i.e. 20) of the line represent the cost to join the service.
So, the answer is option (B).
Question 9
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In a final buzzer round of a competition, contestants were asked to name as many states that begin with the letter $$K$$, by pressing the buzzer as early as possible., The bar graph shows the number of states the contestants were able to name. Find the number of contestants who participated in final buzzer round.

A
$$6$$

B
$$8$$

C
$$14$$

D
$$20$$

Solution

Arranging the data in tabular form gives us

No of states $$\rightarrow$$ 1 2 3 4 5 6 7 8 Total
No of candidates who correctly answered them $$\rightarrow$$ 1 1 5 6 4 0 2 1 20

Hence, the total number of participants were $$20$$.
Question 10
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A random variable $$X$$ has the probability distribution given below. Its variance is
X 1 2 3 4 5
P(X=x) k 2k 3k 2k k

A
$$\dfrac{16}{3}$$

B
$$\dfrac{4}{3}$$

C
$$\dfrac{5}{3}$$

D
$$\dfrac{10}{3}$$

Solution

We know that
$$\sum P(x) = 1$$
$$k+2k+3k+2k+k=1$$
$$9k=1$$
$$k=\frac{1}{9}$$
Now, var $$\sigma^2 = \sum xi^2P(xi)-(\sum\,xiP(xi))^2$$
$$=1(k)+2^2(2k)+3^2(3k)+4^2(2k)+5^2(k)-[1(k)+2(2k)+3(3k)+4(2k)+5(k)]^2$$
$$=93k-(27k)^2$$
$$=93(\cfrac{1}{9})-[27(\frac{1}{9})]^2$$
$$=\cfrac{31}{3}-3^2$$
$$=\cfrac{31-27}{3}$$
$$=\cfrac{4}{3}$$