Statistics Test

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Statistics Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

If t is the standard deviation of x, y, z then the standard deviation of x + 5, y + 5, z + 5 is

A
$$\dfrac{t}{3}$$

B
$$t + 5$$

C
$$t$$

D
$$xyz$$

Solution

$$\text{Standard deviation is invariant under change of origin}$$
$$\text{Hence, standard deviation of x+5,y+5, z+5 is same as x, y, z}$$
$$\Rightarrow \text{ standard deviation of x+5,y+5, z+5 is t}$$.
Option C is correct.
Question 2
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 3
1 / -0

Lowest value of variance can be:

A
$$1$$

B
$$-1$$

C
$$0$$

D
None of these

Solution

We know that $$Var(x)=E(X^2)-(E(x))^2$$

Variance is non-negative because the squares are positive or zero.

Therefore, $$Var(X)\geq 0$$

Hence, the lowest value of variance is $$zero$$
Question 4
1 / -0

Which of the following is not a measure of central location?

A
Mean

B
Median

C
Mode

D
Variance

Solution

Mean, median and mode give us the knowledge about the central value.
But the Variance will give us the deviations from the central tendencies.
Question 5
1 / -0

If $$\mu$$ is the mean distribution of $$\left (Y_{i}, f_{i}\right )$$, then $$\sum f_i(i - \mu)$$ is equal to.

A
$$MD$$

B
$$SD$$

C
$$0$$

D
Relative frequency

Solution

$$\mu $$ is mean distributaion of $$({ y }_{ i },{ f }_{ i })$$
$$\Sigma $$ $${ f }_{ i }(i-\mu )$$ $$=$$ Mean deviation
$$\therefore $$ MD.
Question 6
1 / -0

The largest of $$50$$ measurements is $$3.84$$kg. If the range is $$0.46$$kg, find the smallest measurement.

A
$$3.38$$kg.

B
$$2.38$$kg.

C
$$6.38$$kg.

D
None of these

Solution

$$\Rightarrow$$ Here, $$L=3.84$$ and $$R=0.46$$
$$\Rightarrow$$ $$R=L-S$$
$$0.46=3.84-S$$
$$S=3.84-0.46$$
$$\therefore$$ $$S=3.38\,kg$$
$$\therefore$$ Smallest measurement is $$3.38\,kg$$
Question 7
1 / -0

What is the standard deviation of $$7,9,11,13,15$$?

A
$$2.4$$

B
$$2.5$$

C
$$2.7$$

D
$$2.8$$

Solution

Given numbers are $$ 7,9,11,13,15$$
Mean of given numbers $$=\dfrac { 7+9+11+13+15 }{ 5 } =11$$
Standard deviation$$=\dfrac { |7-11|+|9-11|+|11-11|+|13-11|+|15-11| }{ 5 } =2.4$$
Option A is true
Question 8
1 / -0

Find the range and coefficient of range of the following data. $$59, 46, 30, 23, 27, 40, 52, 35, 29$$

A
$$36, 0.44$$

B
$$32, 0.44$$

C
$$36, 0.84$$

D
None of these

Solution

$$\Rightarrow$$ The given numbers are $$59,46,30,23,27,40,52,35,29$$.
$$\Rightarrow$$ Here, the largest value $$=x_m=59$$ and the smallest value $$=x_0=23$$.
$$\Rightarrow$$ $$Range=x_m-x_0$$
$$=59-23$$
$$=36$$
$$\Rightarrow$$ $$Coefficient\,of\,range=\dfrac{x_m-x_0}{x_m+x_0}$$

$$=\dfrac{59-23}{59+23}$$

$$=\dfrac{36}{82}$$

$$=0.44$$
Question 9
1 / -0

The wickets taken by a bowler in a one-day cricket match are $$4, 5, 6, 3, 4, 0, 3, 2, 3, 5.$$ The mode of the data is ...............

A
$$3$$

B
$$4$$

C
$$5$$

D
$$2$$

Solution

Mode of the set of data is the observation which occurs the most.
$$4$$ and $$6$$ occurs $$2$$ times each, $$6,~2$$ and $$0$$ occurs $$1$$ time each, whereas $$3$$ occurs $$3$$ times.
Thus, the number $$3$$ occurs the maximum number of times i.e., $$3$$.
Therefore, mode of the data is $$3$$.
Question 10
1 / -0

What is the variance of the first $$11$$ natural numbers?

A
$$10$$

B
$$11$$

C
$$12$$

D
$$13$$

Solution

Sum of first $$11$$ natural numbers $$=\dfrac { n(n+1) }{ 2 } =\dfrac { 11\times 12 }{ 2 } =66$$

So, mean $$ =\dfrac { 66 }{ 11 } =6$$

Variance $$= { \dfrac { (1-6)^{ 2 }+(2-6)^{ 2 }+(3-6)^{ 2 }+........+(11-6)^{ 2 } }{ 11 } }$$

$$= { \dfrac { 25+16+9+4+1+0+1+4+9+16+25 }{ 11 } }=\dfrac { 110 }{ 11 } =10$$

Hence, A is correct.

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Re-Attempt Weekly Quiz Competition

Statistics Test - 20

Result

Statistics Test - 20

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SHARING IS CARING

Question 1

$$\dfrac{t}{3}$$

$$t + 5$$

$$t$$

$$xyz$$

Solution

Question 2

$$7$$

$$6$$

$$1$$

$$4$$

Solution

Question 3

$$1$$

$$-1$$

$$0$$

None of these

Solution

Question 4

Mean

Median

Mode

Variance

Solution

Question 5

$$MD$$

$$SD$$

$$0$$

Relative frequency

Solution

Question 6

$$3.38$$kg.

$$2.38$$kg.

$$6.38$$kg.

None of these

Solution

Question 7

$$2.4$$

$$2.5$$

$$2.7$$

$$2.8$$

Solution

Question 8

$$36, 0.44$$

$$32, 0.44$$

$$36, 0.84$$

None of these

Solution

Question 9

$$3$$

$$4$$

$$5$$

$$2$$

Solution

Question 10

$$10$$

$$11$$

$$12$$

$$13$$

Solution

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