Descriptive Statistics Test 25

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Descriptive Statistics Test 25

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Weekly Quiz Competition

Question 1
1 / -0

.

A
5

B
60

C
10

D
12

Solution

$$\Rightarrow$$ One symbol represents $$5$$ balloons.
$$\Rightarrow$$ Then, $$60$$ balloons represents how many symbols.
$$\therefore$$ Required symbols $$=\dfrac{60}{5}=12$$
$$\therefore$$ The number of symbols to be drawn to represent $$60$$ ballons is $$12$$
Question 2
1 / -0

The pictogram shows the number of pupils who cycle to school. What is the total number of pupils who use cycle for going school?

A
$$10$$

B
$$300$$

C
$$420$$

D
$$450$$

Solution

Number of pupils who use cycle for going school in class 1 $$= 30\times 5 = 150 $$
Number of pupils who use cycle for going school in class 1 $$= 30\times 7 = 210 $$
Number of pupils who use cycle for going school in class 1 $$= 30\times 3= 90 $$
So, Total number of pupils who use cycle for going school $$= 150+210+90 = 450$$
Question 3
1 / -0

Given above is a bar graph showing the heights of six mountain peaks. Read the above diagram and answer the following:
Write the ratio of the heights of highest peak and the lowest peak.

A
$$22 : 15$$

B
$$15 : 22$$

C
$$20 : 13$$

D
$$13 : 22$$

Solution

From the above bar graph,
Height of highest peak $$= 8800\ m$$
Height of lowest peak $$= 6000\ m$$

Hence the required ratio will be,
Ratio $$=8800 : 6000$$
$$ = 22 :15$$

Hence, option $$A$$ is correct.
Question 4
1 / -0

Students at a local college were asked how many hours they slept last night. The adjoining chart shows the data . A bar graph of this data will be made on a grid that is 20 units. What scale would be most appropriate for the axis labelled "Number of Students" ?
Hours of Sleep Number of Students
6 14
7 26
8 28
9 15
More than 10 6

A
1 unit = 1 student

B
1 unit = 2 students

C
1 unit = 10 students

D
1 unit = 28 students

Solution

As there are maximum student are 28 so ,"1unit=2 student" is scale would be most appropriate for the axis labelled "Number of Students".
Question 5
1 / -0

Standard deviation of the distribution $$1, 3, 5,....., 13$$ will be

A
$$2$$

B
$$4$$

C
$$7$$

D
None

Solution

Mean of the given numbers is $$\bar x =\dfrac{1+3+5+7+9+11+13}{7}=\dfrac{49}{7}=7$$

total number of values $$n=7$$

Standard deviation is given by $$SD=\sqrt{\dfrac{\sum_{i=1}^n (x_i-\bar x)^2}{n-1}}$$

$$\implies SD=\sqrt{\dfrac{(1-7)^2+(3-7)^2+(5-7)^2+(7-7)^2+(9-7)^2+(11-7)^2+(13-7)^2}{7-1}}$$

$$\implies SD=\sqrt{\dfrac{36+16+4+0+4+16+36}{6}}$$

$$\implies SD=\sqrt{\dfrac{112}{6}}$$

$$\implies SD=\sqrt{18.6667}=4.32$$

Therefore the standard deviation for the given values is $$4.32$$
Question 6
1 / -0

In the following table pass percentage of three schools from the year $$2001$$ to the year $$2006$$ are given. Which school students performance is more consistent?

$$2001$$ $$2002$$ $$2003$$ $$2004$$ $$2005$$ $$2006$$
School (X) $$80$$ $$89$$ $$79$$ $$83$$ $$84$$ $$65$$
School (Y) $$92$$ $$94$$ $$76$$ $$75$$ $$80$$ $$63$$
School (Z) $$93$$ $$97$$ $$67$$ $$63$$ $$70$$ $$85$$

A
X

B
Y

C
Z

D
X and Y

Solution

Average of $$x=\cfrac { 80+89+79+83+84+65 }{ 6 } =\cfrac { 480 }{ 6 } =80$$
Average of $$y=\cfrac { 92+94+76+75+80+63 }{ 6 } =\cfrac { 480 }{ 6 } =80$$
Average of $$z=\cfrac { 93+97+67+63+70+85 }{ 6 } =79.16$$
Average of x and y are equal and more than z.
So,their performance is consistent.
Question 7
1 / -0

Study the graph carefully and answer the questions given below it. What is the total wheat import during all the given years (in thousand tonnes)?

A
$$27420$$

B
$$28240$$

C
$$29240$$

D
$$28420$$

Solution

Total wheat import during all the given years
$$=3465+1811+2413+4203+7016+5832+2000+2500=29240$$ Thousand tonnes
Question 8
1 / -0

Find the standard deviation of $$210, 240, 250, 260, 220, 230$$ and $$270$$.

A
$$18$$

B
$$20$$

C
$$22$$

D
$$25$$

Solution

Mean of the given numbers is $$\bar x =\dfrac{210+240+250+260+220+230+270}{7}=\dfrac{1680}{7}=240$$

total number of values $$n=7$$

Standard deviation is given by $$SD=\sqrt{\dfrac{\sum_{i=1}^n (x_i-\bar x)^2}{n}}$$

$$\implies SD=\sqrt{\dfrac{(210-240)^2+(240-240)^2+.....+(270-240)^2}{7}}$$

$$\implies SD=\sqrt{\dfrac{900+0+100+400+400+100+900}{7}}$$

$$\implies SD=\sqrt{\dfrac{2800}{7}}$$

$$\implies SD=\sqrt{400}=20$$

Therefore the standard deviation for the given values is $$20$$
Question 9
1 / -0

The ages (in years) of a family of 6 members are 1, 5, 12, 15, 38 and 40. The standard deviation is found to be 15.9. After 10 years the standard deviation is

A
increased

B
decreased

C
remains same

D
none of these

Solution

Then mean of six members=$$\frac{1+5+12+15+38+40}{6}=\frac{111}{6}=18.5$$
Then Variance $$\alpha ^{2}=\frac{(18.5-1)^{2}+(18.5-5)^{2}+(18.5-12)^{2}+(18.5-15)^{2}+(18.5-38)^{2}+(18.5-40)^{2}}{5}$$
$$=\frac{(17.5)^{2}+(13.5)^{2}+(6.5)^{2}+(3.5)^{2}+(-19.5)^{2}+(21.5)^{2}}{6}$$
$$=\frac{306.25+182.25+42.25+12.25+380.25++462.25}{6}=\frac{1385.50}{6}=230.91$$
So standard deviation $$\alpha =15.19$$
Given after 10 year The standard deviation is 15.9
Then standard deviation remain same
Question 10
1 / -0

The S.D. of the following freq. dist.
Class 0-10 10-20 20-30 30-40
$$f_i$$ 1 3 4 2

A
$$7.8$$

B
$$9$$

C
$$8.1$$

D
$$0.9$$

Solution

Class $$x_i$$ $$f_i$$ $$u_i=\dfrac{x_i-A}{h}$$ $$u_i^2$$ $$f_iu_i$$ $$f_iu_i^2$$
0-10 5 1 -2 4 -2 4
10-20 15 3 -1 1 -3 3
20-30 25 4 0 0 0 0
30-40 35 2 1 1 2 2
Total 10 -3 9
$$S.D.$$$$=h\sqrt { \cfrac { \sum { { f }_{ i }{ u }_{ i }^{ 2 } } }{ \sum { { f }_{ i } } } -{ \left( \cfrac { \sum { f } _{ i }{ u }_{ i } }{ \sum { { f }_{ i } } } \right) }^{ 2 } } $$
$$S.D.=10\sqrt { \cfrac { 9 }{ 10 } -{ \left( \cfrac { -3 }{ 10 } \right) }^{ 2 } } =9$$

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Re-Attempt Weekly Quiz Competition

	$$2001$$	$$2002$$	$$2003$$	$$2004$$	$$2005$$	$$2006$$
School (X)	$$80$$	$$89$$	$$79$$	$$83$$	$$84$$	$$65$$
School (Y)	$$92$$	$$94$$	$$76$$	$$75$$	$$80$$	$$63$$
School (Z)	$$93$$	$$97$$	$$67$$	$$63$$	$$70$$	$$85$$

Class	$$x_i$$	$$f_i$$	$$u_i=\dfrac{x_i-A}{h}$$	$$u_i^2$$	$$f_iu_i$$	$$f_iu_i^2$$
0-10	5	1	-2	4	-2	4
10-20	15	3	-1	1	-3	3
20-30	25	4	0	0	0	0
30-40	35	2	1	1	2	2
Total		10			-3	9

Hours of Sleep	Number of Students
6	14
7	26
8	28
9	15
More than 10	6

Descriptive Statistics Test 25

Result

Descriptive Statistics Test 25

Score

-

Rank

-

SHARING IS CARING

Question 1

5

60

10

12

Solution

Question 2

$$10$$

$$300$$

$$420$$

$$450$$

Solution

Question 3

$$22 : 15$$

$$15 : 22$$

$$20 : 13$$

$$13 : 22$$

Solution

Question 4

1 unit = 1 student

1 unit = 2 students

1 unit = 10 students

1 unit = 28 students

Solution

Question 5

$$2$$

$$4$$

$$7$$

None

Solution

Question 6

X

Y

Z

X and Y

Solution

Question 7

$$27420$$

$$28240$$

$$29240$$

$$28420$$

Solution

Question 8

$$18$$

$$20$$

$$22$$

$$25$$

Solution

Question 9

increased

decreased

remains same

none of these

Solution

Question 10

$$7.8$$

$$9$$

$$8.1$$

$$0.9$$

Solution

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