Descriptive Statistics Test 36

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Descriptive Statistics Test 36

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Weekly Quiz Competition

Question 1

1 / -0

Directions For Questions

The number of hours for which students of a particular class watched television during holidays is shown through the given graph.

Answer the following questions:

...view full instructions

The hours in which maximum number of students watched TV , is ______ .

$$3-4$$ hours

$$5-6$$ hours

$$4-5$$ hours

$$2-3$$ hours

Solution

Hours of TV Watched	Number of Students
1-2	4
2-3	8
3-4	22
4-5	32
5-6	8
6-7	6

As clearly seen from the Graph and Corresponding Table,

Maximum number of Students watched TV between $$4$$-$$5$$ Hours.

Question 2
1 / -0

What is the ratio of the highest marks to the lowest marks obtained by the student?

A
$$2 : 11$$

B
$$9 : 2$$

C
$$2 : 9$$

D
$$11 : 2$$

Solution

According to bargraph, his scores are as follows :
English $$= 55$$
Mathematics $$= 90$$
Hindi $$= 40$$
Science $$= 80$$
History $$= 20$$

Highest marks obtained in Mathematics $$= 90$$
Lowest marks are obtained in History $$= 20$$

Ratio $$= 90:20 = 9:2$$
Question 3
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What is the average marks obtained by the student?

A
$$57$$

B
$$63$$

C
$$80$$

D
$$48$$

Solution

According to bargraph, his scores are as follows :
English $$= 55$$
Mathematics $$= 90$$
Hindi $$= 40$$
Science $$= 80$$
History $$= 20$$

Total marks obtained $$= 55+90+40+80+20 = 285$$
Average marks obtained $$=$$ Total Marks $$\div$$ Number of subjects

$$\Rightarrow$$ Average marks obtained $$= \dfrac{285}{5} = 57$$
Question 4
1 / -0

The sale of electric fans on different days of the week is shown above. Observe the pictograph and answer the following questions.
If one fan was sold of $$900.$$ What were the total earnings on Friday?

A
$$6300$$

B
$$6500$$

C
$$18900$$

D
$$21000$$

Solution

There are $$7$$ images of fan in the row of Friday and $$1$$ fan corresponds to $$3$$ units so,
Number of fans sold $$=$$ $$3\times 7$$
$$=21$$

Cost of $$1$$ fan $$= 900$$
$$\therefore$$ Cost of $$21$$ fans $$= 21\times 900$$
$$ = 18900$$
Question 5
1 / -0

The average marks of $$10$$ students in a class was $$60$$ with standard deviation $$4$$. While the average marks of other $$10$$ students was $$40$$ with a standard deviation $$6$$. If all the $$20$$ students are taken together, their standard deviation will be.

A
$$5.0$$

B
$$7.5$$

C
$$9.8$$

D
$$11.5$$

Solution

Here,
$$n_1=10,\overline{x}_1=60$$ and $$\sigma_1=4$$
$$\therefore$$ $$\sum x_i=60\times 10=600$$
Now, $$n_2=10,\overline{x}_2=40$$ and $$\sigma_2=6$$
$$\therefore$$ $$\sum x_i=10\times 40=400$$
$$\Rightarrow$$ Total marks of $$20$$ students $$(\sum_{i=1}^{20} x)=400+600=1000$$
$$\Rightarrow$$ $$\overline{x}=\dfrac{1000}{20}=50$$

Now, $$\sigma_1^2=(4)^2$$
$$\Rightarrow$$ $$\dfrac{1}{n_1}\sum_{i=1}^{10}x_i^2-(\overline{x_1})^2=16$$
$$\Rightarrow$$ $$\sum_{i=1}^{10}x_i^2=n_1(16+(\overline{x_1})^2)$$
$$=10(16+3600)$$
$$\Rightarrow$$ $$\sum_{i=1}^{10}x_i^2=36160$$

Now, $$\sigma_2^2=(6)^2$$
$$\Rightarrow$$ $$\dfrac{1}{n_2}\sum_{i=11}^{20}x_i^2-(\overline{x_2})^2=36$$

$$\Rightarrow$$ $$\sum_{i=11}^{20}x_i^2=(36+(\overline{x_2})^2)n_2$$
$$=(36+1600)10$$
$$\Rightarrow$$ $$\sum_{i=11}^{20}x_i^2=16360$$
Now, required standard deviation $$(\sigma)=\sqrt{\dfrac{1}{n}\sum x_i^2-\overline{x}^2}$$

$$=\sqrt{\dfrac{1}{20}(36160+16360)-(50)^2}$$
$$=\sqrt{2626-2500}$$
$$=\sqrt{126}$$
$$=11.2$$
Question 6
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Direction (10-13) : The given bar graph shows the marks obtained by a student in different subjects. The maximum marks of each subject is $$100$$.
What is the ratio of the highest marks to the lowest marks obtained by the student?

A
$$2 : 11$$

B
$$9 : 2$$

C
$$2 : 9$$

D
$$11 : 2$$

Solution

Highest marks obtained by student $$= 90$$
Lowest marks obtained by student $$= 20$$
Thus ratio $$= 90 : 20 = 9 : 2$$

Question 7

1 / -0

The pictograph shows different subject books which are kept in a library. Observe the graph and answer the following question:
How many more Science books than the History books are there in the library?

$$400$$

$$200$$

$$300$$

$$500$$

Solution

$$\Rightarrow$$ In pictograph, one book symbol equal to $$100$$ books.

$$\therefore$$ From given pictograph, we have made following frequency distribution table :

$$Subject$$	$$No.of\,books$$
$$Hindi$$	$$6\times 100=600$$
$$English$$	$$8\times 100=800$$
$$History$$	$$2\times 100=200$$
$$Science$$	$$4\times 100=400$$
$$Maths$$	$$3\times 100=300$$
$$Total$$	$$2300$$

$$\Rightarrow$$ Number of science books in library $$=400$$

$$\Rightarrow$$ Number of History books in library $$=200$$

$$\Rightarrow$$ Difference between science and history books $$=400-200=200$$

$$\therefore$$ In library, there are $$200$$ science books more than history books.

Question 8
1 / -0

Direction (9-10) : Following pictograph shows the number of tractors in five villages. Observer the pictograph and answer the following questions.
How many villages have 6 number of tractors?

A
4

B
3

C
2

D
5

Solution

$$\Rightarrow$$ From pictograph we have made following frequency distribution table :

$$Villages$$ $$No.\,of\,Tractors$$
$$A$$ $$6$$
$$B$$ $$5$$
$$C$$ $$8$$
$$D$$ $$3$$
$$E$$ $$6$$
$$Total$$ $$28$$
$$\Rightarrow$$ From above table we can see, village $$A,C$$ and village $$E$$ have same number of tractors i.e. $$6$$
$$\therefore$$ Number of villages have 6 number of tractor is $$3$$.
Question 9
1 / -0

Direction (16-17) : The pictograph shows different subject books which are kept in a library. Observe the graph and answer the following questions.
How many English books are there in the library?

A
800

B
700

C
500

D
600
Question 10
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The given bar graph shows the marks obtained by a student in different subjects. The maximum marks of each subject is 100.
In which subject did the student score highest marks?

A
English

B
Mathematics

C
Science

D
S.St

Solution

Given graph shows the marks obtained in different subjects.

From the graph, the highest marks are $$90$$ which is obtained in Mathematics

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Re-Attempt Weekly Quiz Competition

$$Villages$$	$$No.\,of\,Tractors$$
$$A$$	$$6$$
$$B$$	$$5$$
$$C$$	$$8$$
$$D$$	$$3$$
$$E$$	$$6$$
$$Total$$	$$28$$

Descriptive Statistics Test 36

Result

Descriptive Statistics Test 36

Score

-

Rank

-

SHARING IS CARING

Question 1

$$3-4$$ hours

$$5-6$$ hours

$$4-5$$ hours

$$2-3$$ hours

Solution

Question 2

$$2 : 11$$

$$9 : 2$$

$$2 : 9$$

$$11 : 2$$

Solution

Question 3

$$57$$

$$63$$

$$80$$

$$48$$

Solution

Question 4

$$6300$$

$$6500$$

$$18900$$

$$21000$$

Solution

Question 5

$$5.0$$

$$7.5$$

$$9.8$$

$$11.5$$

Solution

Question 6

$$2 : 11$$

$$9 : 2$$

$$2 : 9$$

$$11 : 2$$

Solution

Question 7

$$400$$

$$200$$

$$300$$

$$500$$

Solution

Question 8

4

3

2

5

Solution

Question 9

800

700

500

600

Question 10

English

Mathematics

Science

S.St

Solution

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