Statistics Test

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Statistics Test - 26

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Weekly Quiz Competition

Question 1

1 / -0

Directions For Questions

Study the following table and answer the questions based on it.
Expenditure of a Company (in Lakh Rupees) per Annum Over the given years.

Year	Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
$$1998$$	$$288$$	$$98$$	$$3.00$$	$$23.4$$	$$83$$
$$1999$$	$$342$$	$$112$$	$$2.52$$	$$32.5$$	$$108$$
$$2000$$	$$324$$	$$101$$	$$3.84$$	$$41.6$$	$$74$$
$$2001$$	$$336$$	$$133$$	$$3.68$$	$$36.4$$	$$88$$
$$2002$$	$$420$$	$$142$$	$$3.96$$	$$49.4$$	$$98$$

...view full instructions

What is the average amount of interest per year which the company had to pay during this period?

$$Rs. 32.43$$ lakhs

$$Rs. 33.72$$ lakhs

$$Rs. 34.18$$ lakhs

$$Rs. 36.66$$ lakhs

Solution

Average amount of interest paid by the Company during the given period
$$= Rs. \left [\dfrac {23.4 + 32.5 + 41.6 + 36.4 + 49.4}{5}\right ]lakhs$$
$$= Rs. \left [\dfrac {183.3}{5}\right ]lakhs$$
$$= Rs. 36.66\ lakhs$$

Question 2
1 / -0

Mean of marks obtained by $$10$$ students is $$30$$.
Marks obtained are $$25,30,21,55,47,10,15,x,45,35$$.
Find the value of $$x$$.

A
$$25$$

B
$$37$$

C
$$69$$

D
$$17$$

Solution

Let $$u$$ be the average marks of the class.
$$\therefore u=\dfrac{25+30+21+55+47+10+15+x+45+35}{10}=\dfrac{283+x}{10}$$
But $$u=30$$.
So,$$30=\dfrac{283+x}{10}$$.
$$\therefore x=17$$
Ans-Option D
Question 3
1 / -0

Find AM of divisors of $$100$$.

A
$$24$$

B
$$25.5$$

C
$$24.11$$

D
$$21.9$$

Solution

Divisors of 100 are:
$$1, 2, 4, 5, 10, 20, 25, 50, 100$$
$$\therefore n=9$$
$$\therefore S=1+2+4+5+10+20+25+50+100=217$$
$$\therefore A.M.=\dfrac{S}{n}=\dfrac{217}{9}=24.11$$
Question 4
1 / -0

If the Arithmetic mean of $$8, 6, 4, x, 3, 6, 0$$ is $$4$$; then the value of $$x =$$

A
$$7$$

B
$$6$$

C
$$1$$

D
$$4$$

Solution

Arithmetic mean $$= \cfrac{\text{sum of all observations}}{\text{no. of observations}}$$
$$\Rightarrow 4=\cfrac { 8+6+4+x+3+6+0 }{ 7 } \\ \Rightarrow 28=27+x\\ \Rightarrow x=1$$
Question 5
1 / -0

Directions For Questions

$$0-9$$ $$40$$
$$10-19$$ $$50$$
$$20-29$$ $$70$$
$$30-39$$ $$40$$

This shows the distribution of students and the number of hours they work.

...view full instructions

The relative frequency of students working $$9$$ hours or less is

A
$$2$$

B
$$40$$

C
$$45$$

D
Can not be determined from the information given.

Solution

The relative frequency of students working $$9$$ hours or less lie in the $$0-9$$ hours group.
So, total number of students $$=40$$.
Question 6
1 / -0

Mean of $$40$$ observations was given as $$160$$.It was detected that $$125$$ was misread as $$160$$. Find the correct mean.

A
$$158$$

B
$$169$$

C
$$159$$

D
$$161$$

Solution

Formula used:
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$
Sine, number of observations$$,n=40$$
Mean$$=160$$ (initial wrong mean)
Incorrected sum$$=n \times u=40 \times 160=6400$$
Now $$125$$ was read as $$165$$, so
Corrected sum $$=6400-165+125=6360$$
$$\therefore$$ Corrected mean $$=\dfrac{6360}{40} =159$$
Question 7
1 / -0

The histogram shows the birth weights of 100 new born babies.
How many babies weighed 8 lb or more?

A
$$23$$

B
$$45$$

C
$$30$$

D
$$22$$

Solution

Given graph shows birth weights of 100 new born babies

From the graph, the number of babies whose weight is $$8\ lb$$ or more is $$22+16+6+1=45$$
Question 8
1 / -0

Directions For Questions

$$0-9$$ $$40$$
$$10-19$$ $$50$$
$$20-29$$ $$70$$
$$30-39$$ $$40$$

This shows the distribution of students and the number of hours they work.

...view full instructions

Find the number of students working $$19$$ hours or less.

A
$$40$$

B
$$50$$

C
$$90$$

D
Can not be determined without the original data

Solution

The number of students working $$19$$ hours or less will contain the group which works for $$0-9$$ hours as well as $$10-19$$ hours.
So, total students $$=40+50=90$$.
Question 9
1 / -0

The mean age of $$25$$ students in a class is $$12$$. If the teacher's age is included, the mean age increases by $$1$$. Then teacher's age (in years) is:

A
$$24$$

B
$$38$$

C
$$30$$

D
$$48$$

Solution

Sum of $$25$$ students ages be $$x$$

$$\Rightarrow $$ Mean $$=\dfrac {x}{25}=12\Rightarrow x=300$$ equation - (1)

Let the teacher's age be $$y$$

$$\Rightarrow $$ New mean $$=\dfrac {x+y} {26}=13$$

$$\Rightarrow 300+y=338$$

$$\Rightarrow y=38$$

Teacher's age $$=y=38$$
Question 10
1 / -0

The mean salary paid per week to $$1000$$ employees of an establishment was found to be Rs. $$900$$. Later on, it was discovered that the salaries of two employees were wrongly recorded as Rs. $$750$$ and Rs. $$365$$ instead of Rs. $$570$$ and Rs. $$635$$. Find the corrected mean salary.

A
$$900.90$$

B
$$1,115$$

C
$$1,225$$

D
$$900.09$$

Solution

We first find the corrected sum of observation.
Corrected sum of observations$$=$$(Sum of total incorrect observation)$$-$$(Sum of incorrect data)$$+$$(Sum of correct data).
$$=900\times 1,000-(750+365)+(570+635)=9,00,090$$
$$\therefore$$ Corrected Mean $$=Rs.\dfrac{9,00,090}{1,000}=Rs.900.09$$

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Re-Attempt Weekly Quiz Competition

$$0-9$$	$$40$$
$$10-19$$	$$50$$
$$20-29$$	$$70$$
$$30-39$$	$$40$$

$$0-9$$	$$40$$
$$10-19$$	$$50$$
$$20-29$$	$$70$$
$$30-39$$	$$40$$

Statistics Test - 26

Result

Statistics Test - 26

Score

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Rank

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SHARING IS CARING

Question 1

$$Rs. 32.43$$ lakhs

$$Rs. 33.72$$ lakhs

$$Rs. 34.18$$ lakhs

$$Rs. 36.66$$ lakhs

Solution

Question 2

$$25$$

$$37$$

$$69$$

$$17$$

Solution

Question 3

$$24$$

$$25.5$$

$$24.11$$

$$21.9$$

Solution

Question 4

$$7$$

$$6$$

$$1$$

$$4$$

Solution

Question 5

$$2$$

$$40$$

$$45$$

Can not be determined from the information given.

Solution

Question 6

$$158$$

$$169$$

$$159$$

$$161$$

Solution

Question 7

$$23$$

$$45$$

$$30$$

$$22$$

Solution

Question 8

$$40$$

$$50$$

$$90$$

Can not be determined without the original data

Solution

Question 9

$$24$$

$$38$$

$$30$$

$$48$$

Solution

Question 10

$$900.90$$

$$1,115$$

$$1,225$$

$$900.09$$

Solution

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