Statistics Test

Result

Statistics Test - 34

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Suppose for $$40$$ observations, the variance is $$50$$. If all the observations are increased by $$20$$, the variance of these increased observation will be

A
$$20$$

B
$$50$$

C
$$30$$

D
None of these

Solution

The variance for $$40$$ observations is $$50$$
Variance is independent of the number of observations. Therefore, variance for $$60$$ observations is $$50$$
Question 2
1 / -0

Variance of the first $$11$$ natural numbers is:

A
$$\sqrt{5}$$

B
$$\sqrt{10}$$

C
$$5\sqrt{2}$$

D
$$10$$

Solution

Sum of first $$n$$ natural numbers is $$\dfrac {n^2-1}{12}$$
$$=\dfrac {11^2-1}{12}$$
$$=\dfrac {120}{12}$$
$$=10$$
Thus, variance is $$\sqrt {\dfrac {n^2-1}{12}}$$ $$=\sqrt {10}$$.
Question 3
1 / -0

If a, b are constants then, $$Var(a+bX)$$ is

A
$$Var(a)+Var(X)$$

B
$$Var(a)-Var(X)$$

C
$$b^2Var(X)$$

D
None of these

Solution

$$Var(a+bX)=Var(a)+Var(bX)$$

$$\implies Var(a+bX)=0+Var(bX)$$ (Since, $$Var(c)=0$$)

$$\implies Var(a+bX)=b^2Var(X)$$ (Since, $$Var(aX)=a^2Var(X)$$)
Question 4
1 / -0

If $$X, Y $$ are independent then $$SD(X-Y)$$ is:

A
$$SD(X)-SD(Y)$$

B
$$SD(X)+SD(Y)$$

C
$$\sqrt{SD(X)+SD(Y)}$$

D
None of these

Solution

$$SD(X-Y)=SD(X)+SD(-Y)$$

$$\implies SD(X-Y)=SD(X)+SD(Y)$$ (since, $$SD(aX)=|a|SD(X)$$)
Question 5
1 / -0

If the standard deviation of a population is $$9$$, the population variance is:

A
$$9$$

B
$$3$$

C
$$21$$

D
$$81$$

Solution

We know that variance is square of standard deviation.

Given that standard deviation is $$9$$

Therefore, variance $$=9^2=81$$
Question 6
1 / -0

If total sum of square is $$20$$ and sample variance is $$5$$ then total number of observations are

A
$$15$$

B
$$35$$

C
$$25$$

D
$$4$$

Solution

We know that variance is $$\dfrac{\text{sum of the squares}}{\text{total observations}}$$

Given that sum of squares is $$20$$ and
the variance is $$5$$

Therefore, $$5=\dfrac{20}{\text{total observations}}$$

$$\implies \text{total observations}=\dfrac{20}5=4$$
Question 7
1 / -0

Find $$Var(2X+3)$$

A
$$5 Var(X)+3$$

B
$$4 Var(X)+3$$

C
$$4 Var(X)$$

D
None of these

Solution

$$Var(2X+3)=Var(2X)+Var(3)$$

$$\implies Var(2X+3)=Var(2X)+0$$ (Since, $$Var(c)=0$$)

$$\implies Var(2X+3)=2^2Var(X)$$ (Since, $$Var(aX)=a^2Var(X)$$)

$$\implies Var(2X+3)=4Var(X)$$
Question 8
1 / -0

If the standard deviation of a set of scores is $$1.2$$ and their mean is $$10$$, then the coefficient of variation of the scores is

A
$$12$$

B
$$0.12$$

C
$$20$$

D
$$120$$

Solution

Given : standard deviation$$(\sigma)=1.2,$$ mean$$(\overline {X})=10$$.
Coefficient of variation(C.V.) $$=\dfrac{\sigma}{\overline {X}}\times 100=\dfrac{1.2}{10}\times 100=12$$
$$\therefore$$ C.V. $$=12$$
Hence, option $$A$$ is correct.
Question 9
1 / -0

Calculate the standard deviation of the first $$13$$ natural numbers.

A
$$3.74$$.

B
$$2.74$$.

C
$$3.48$$.

D
None of these

Solution

$$\Rightarrow$$ $$1st$$ $$13$$ natural numbers are $$1,2,3,4,5,6,7,8,9,10,11,12,13.$$
$$\sum x=\dfrac{n(n+1)}{2}$$
$$=\dfrac{13(13+1)}{2}$$
$$=\dfrac{13\times 14}{2}$$
$$\therefore$$ $$\sum x=91$$
Now, $$\sum x^2=\dfrac{n(n+1)(2n+1)}{6}$$
$$=\dfrac{13\times 14\times 27}{6}$$
$$\therefore$$ $$\sum x^2=819$$
$$\Rightarrow$$ $$SD=\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{\sum x}{n}\right)^2}$$
$$=\sqrt{\dfrac{819}{13}-\left(\dfrac{91}{13}\right)^2}$$
$$=\sqrt{63-49}$$
$$=\sqrt{14}$$
$$=3.74$$
Question 10
1 / -0

If the variance of a data is $$12.25$$, then the standard deviation is

A
$$3.5$$

B
$$3$$

C
$$2.5$$

D
$$3.25$$

Solution

$$S.D=\sqrt{variance}$$
$$\Rightarrow S.D=\sqrt{12.25}$$
$$\Rightarrow S.D=3.5$$
Option A is correct.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Statistics Test - 34

Result

Statistics Test - 34

Score

-

Rank

-

SHARING IS CARING

Question 1

$$20$$

$$50$$

$$30$$

None of these

Solution

Question 2

$$\sqrt{5}$$

$$\sqrt{10}$$

$$5\sqrt{2}$$

$$10$$

Solution

Question 3

$$Var(a)+Var(X)$$

$$Var(a)-Var(X)$$

$$b^2Var(X)$$

None of these

Solution

Question 4

$$SD(X)-SD(Y)$$

$$SD(X)+SD(Y)$$

$$\sqrt{SD(X)+SD(Y)}$$

None of these

Solution

Question 5

$$9$$

$$3$$

$$21$$

$$81$$

Solution

Question 6

$$15$$

$$35$$

$$25$$

$$4$$

Solution

Question 7

$$5 Var(X)+3$$

$$4 Var(X)+3$$

$$4 Var(X)$$

None of these

Solution

Question 8

$$12$$

$$0.12$$

$$20$$

$$120$$

Solution

Question 9

$$3.74$$.

$$2.74$$.

$$3.48$$.

None of these

Solution

Question 10

$$3.5$$

$$3$$

$$2.5$$

$$3.25$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.