Statistics Test

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Statistics Test - 25

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Weekly Quiz Competition

Question 1
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Directions For Questions

The histogram shows the number of music directors and the number of songs they complete in a year.

...view full instructions

Find the number of songs made during the interval $$5-6$$.

A
$$20$$

B
$$15$$

C
$$6$$

D
$$8$$

Solution

The height of the bar represents the number of songs.
So, $$20$$ songs were made during the interval $$5-6$$.
Question 2
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Directions For Questions

Judah recorded the number of football tickets collected by his friends, on the histogram.

...view full instructions

In which frequency the number of tickets were same?

A
$$2-4$$ and $$17-19$$

B
$$5-7$$ and $$8-10$$

C
$$8-10$$ and $$11-13$$

D
$$14-16$$ and $$17-19$$

Solution

The number of tickets are same in the frequency $$2-4$$ and $$17-19$$.
Question 3
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Judah recorded the number of football tickets collected by his friends, on the histogram.

What is the total number of tickets collected by Judah between the interval $$8-10$$?

A
$$5$$

B
$$15$$

C
$$10$$

D
$$40$$

Solution

The total number of tickets collected by Judah between the interval $$8-10 = 10 $$
Question 4
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$$12-n, 12, 12+n$$
What is the average (arithmetic mean) of the $$3$$ quantities in the list above?

A
$$4$$

B
$$12$$

C
$$18$$

D
$$4+\dfrac{n}{3}$$

E
$$12+\dfrac{n}{3}$$

Solution

Given $$3$$ Quantities: $$12$$ $$-$$ $$n$$, $$12$$, $$12$$ $$+$$ $$n$$

Average of the above $$3$$ Quantities $$=$$ $$\dfrac {\text{Sum of the above}\: 3\: \text{Quantities}} {\text{Number of Quantities}} $$

$$=$$ $$\dfrac { 12 \space - \space n \space + \space 12 \space + \space 12 \space + \space n }{3}$$

$$=$$ $$\dfrac {12 \times 3}{3}$$

$$=$$ $$12$$

Therefore, average of the Quantities listed above is $$12$$.
Question 5
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Find the average of the expressions $$2x+4, 5x-1$$ and $$-x+3$$.

A
$$x+2$$

B
$$x-2$$

C
$$2x+2$$

D
$$2x-2$$

Solution

Average of the expression $$=$$ $$\dfrac{sum \quad of \quad expression }{total \quad no. \quad of \quad expressions}$$
$$\Rightarrow \dfrac{2x+4+5x-1-x+3}{3}$$
$$\Rightarrow \dfrac{6x+6}{3}$$
$$\Rightarrow \dfrac{3(2x+2)}{3}=2x+2$$
Question 6
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In the graph you can find the takings of a chocolate bar for $$8$$ months. Answer the following question:
In which two months, $$40000$$ chocolate bars are taken out?

A
Jan and Feb

B
Feb and May

C
May and Apr

D
Jun and Jul

Solution

From the given frequency polygon,
Number of chocolates taken in Jan $$=50000$$
Number of chocolates taken in Feb $$=40000$$
Number of chocolates taken in Mar $$=35000$$
Number of chocolates taken in Apr $$=45000$$
Number of chocolates taken in May $$=40000$$
Number of chocolates taken in June $$=50000$$
Number of chocolates taken in Jul $$=60000$$
Number of chocolates taken in Aug $$=60000$$.

Clearly, we can say Feb and May months shows the same number of chocolates, i.e. $$40000$$ chocolates.
So, in the months of Feb and May, $$40000$$ chocolate bars are taken out.

Hence, option $$B$$ is correct.
Question 7
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The mean of $$a, b, c, d$$ and $$e$$ is $$28$$. If the mean of $$a, c$$ and $$e$$ is $$24$$, what is the mean of $$b$$ and $$d$$?

A
$$31$$

B
$$32$$

C
$$33$$

D
$$34$$

Solution

Formula used:
$$\text{Arithmetic mean}= \dfrac{\text{Sum of given numbers}}{\text{Total numbers}}$$

Given $$\Rightarrow$$ $$\dfrac{a+b+c+d+e}{5}=28$$ and $$\dfrac{a+c+e}{3} =24 $$
To find $$\Rightarrow$$ $$\dfrac{b+d}{2}$$ which is nothing but the mean of $$b$$ and $$d$$.

$$\begin{aligned}{}\dfrac{{a + b + c + d + e}}{5} &= 28\\a + b + c + d + e& = 140\quad \dots (i)\end{aligned}$$

Also,
$$\begin{aligned}{}\dfrac{{a + c + e}}{3} &= 24\\a + c + e& = 72\quad \dots (ii)\end{aligned}$$

By using $$(i)$$ and $$(ii)$$,
$$\begin{aligned}{}a + b + c + d + e &= 140\\b + d + 72 &= 140\\b + d &= 68\\\dfrac{{b + d}}{2} &= 34\end{aligned}$$

Hence, option $$D$$ is the correct answer.

Question 8

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Directions For Questions

Study the following table and answer the questions based on it.
Number of Candidates Appeared, Qualified and Selected in a Competitive Examination from Five States Delhi, H.P, U.P, Punjab and Haryana Over the Years $$1994$$ to $$1998$$

		Delhi			H.P.			U.P			Punjab			Haryana
Year	App	Qual	Sel	App	Qual	Sel	App	Qual	Sel	App	Qual	Sel	App	Qual	Sel
$$1997$$	$$8000$$	$$850$$	$$94$$	$$7800$$	$$810$$	$$82$$	$$7500$$	$$720$$	$$79$$	$$8200$$	$$680$$	$$85$$	$$6400$$	$$700$$	$$75$$
$$1998$$	$$4800$$	$$500$$	$$48$$	$$7500$$	$$800$$	$$65$$	$$5600$$	$$620$$	$$85$$	$$6800$$	$$600$$	$$70$$	$$7100$$	$$650$$	$$75$$
$$1999$$	$$7500$$	$$640$$	$$82$$	$$7400$$	$$560$$	$$70$$	$$4800$$	$$400$$	$$48$$	$$6500$$	$$525$$	$$65$$	$$5200$$	$$350$$	$$55$$
$$2000$$	$$9500$$	$$850$$	$$90$$	$$8800$$	$$920$$	$$86$$	$$7000$$	$$650$$	$$70$$	$$7800$$	$$720$$	$$84$$	$$6400$$	$$540$$	$$60$$
$$2001$$	$$9000$$	$$800$$	$$70$$	$$7200$$	$$850$$	$$75$$	$$8500$$	$$950$$	$$80$$	$$5700$$	$$485$$	$$60$$	$$4500$$	$$600$$	$$75$$

...view full instructions

For which state the average number of candidates selected over the years is the maximum?

Delhi

H.P

U.P

Punjab

Solution

The average number of candidates selected over the given period for various states are:

For Delhi $$= \dfrac {94 + 48 + 82 + 90 + 70}{5} $$

$$= \dfrac {385}{5} = 76.8$$

For U.P. $$= \dfrac {78 + 85 + 48 + 70 + 80}{5} $$

$$= \dfrac {361}{5} = 72.2$$

For Punjab $$= \dfrac {85 + 70 + 65 + 84 + 60}{5} $$

$$= \dfrac {364}{5} = 72.8$$

For Haryana $$= \dfrac {75 + 75 + 55 + 60 + 75}{5} $$

$$= \dfrac {340}{5} = 68$$

The average is maximum for Delhi.

Question 9
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The librarian at the public library counted the number of books on each shelf. The highest number of books contained by any of the self is:

A
$$0$$

B
$$2$$

C
$$6$$

D
$$8$$

Solution

On looking the graph, we can say that the books are high at the intervals $$11-20$$ and $$71-80$$ as $$6$$ (The highest bar has the highest frequency).

Hence, option $$C$$ is correct.
Question 10
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A factory kept track of the number of broken plates per shipment last month. Which range of broken plates per shipment occurred more frequently?

A
$$10-19$$

B
$$40-49$$

C
$$30-39$$

D
$$20-29$$

Solution

From the histogram, the number of shipment per range of broken plates:
$$0-9$$ is $$8$$
$$10-19$$ is $$7$$
$$20-29$$ is $$1$$
$$30-39$$ is $$6$$
$$40-49$$ is $$10$$
$$50-59$$ is $$6$$
$$60-69$$ is $$7$$
$$70-79$$ is $$7$$.

The range of broken plates per shipment occurred more frequently $$= 40-49$$, i.e. $$10$$ (The longest bar has the most frequency).

Hence, option $$B$$ is correct.

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Re-Attempt Weekly Quiz Competition

Statistics Test - 25

Result

Statistics Test - 25

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SHARING IS CARING

Question 1

$$20$$

$$15$$

$$6$$

$$8$$

Solution

Question 2

$$2-4$$ and $$17-19$$

$$5-7$$ and $$8-10$$

$$8-10$$ and $$11-13$$

$$14-16$$ and $$17-19$$

Solution

Question 3

$$5$$

$$15$$

$$10$$

$$40$$

Solution

Question 4

$$4$$

$$12$$

$$18$$

$$4+\dfrac{n}{3}$$

$$12+\dfrac{n}{3}$$

Solution

Question 5

$$x+2$$

$$x-2$$

$$2x+2$$

$$2x-2$$

Solution

Question 6

Jan and Feb

Feb and May

May and Apr

Jun and Jul

Solution

Question 7

$$31$$

$$32$$

$$33$$

$$34$$

Solution

Question 8

Delhi

H.P

U.P

Punjab

Solution

Question 9

$$0$$

$$2$$

$$6$$

$$8$$

Solution

Question 10

$$10-19$$

$$40-49$$

$$30-39$$

$$20-29$$

Solution

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