Statistics Test

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Statistics Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

The variance of six observations is given as $$16$$ and mean is $$8$$. If each observation is multiplied by $$3$$.
Find the new variance:

A
$$155$$

B
$$124$$

C
$$177$$

D
$$144$$

Solution

Mean, $$u=8$$.
So, $$\dfrac{x_1+x_2...x_6}{6}=8$$.
$$\therefore x_1+x_2...x_6=48$$.
Multiplying the above equation by $$3$$ on both the sides we get,
$$3x_1+3x_2...3x_6=48\times 3$$
$$\therefore u'=\dfrac{3x_1+3x_2....3x_6}{6}=\dfrac{48 \times 3}{6}$$
$$\therefore u'=24$$
Thus, new mean, $$u'=24$$.
$$\therefore$$ New variance, $$\sigma ^2=\dfrac{(3x_1)^2+...(3x_6)^2}{6}-(24)^2$$
$$\therefore \sigma ^2=9\times \dfrac{(x_1)^2+....(x_6)^2}{6}-576$$
$$\therefore \sigma ^2=9\times \dfrac{480}{16}-576$$
$$\therefore \sigma ^2=720-576$$
$$\therefore \sigma ^2=144$$
Thus, New Variance is $$144$$.
Ans-Option $$D$$
Question 2
1 / -0

Find the variance of the following data:
$$5,9,8,12,6,10,6,8$$

A
$$4.765$$

B
$$4.750$$

C
$$4.450$$

D
$$4.420$$

Solution

Here $$n=8$$.
Mean, $$u=\dfrac{\sum x_i}{n}=\dfrac{64}{8}=8$$
Value of Deviations $$(x_i-u)$$ are
$$-3,1,0,4,-2,2,-2,0$$
Variance, $$\sigma ^2=\dfrac{\sum(x_i-u)^2}{n}=\dfrac{38}{8}=4.75$$.
Ans- Option $$B$$.
Question 3
1 / -0

$$x_i$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$
$$f_i$$ $$6$$ $$8$$ $$15$$ $$25$$ $$8$$ $$4$$
Find the Mean Deviation (M.D) about the mean

A
$$2.1$$

B
$$2.25$$

C
$$2.09$$

D
$$2.71$$

Solution

Total Frequency, $$N=\sum f_i=66$$.
Mean, $$u=\dfrac{(\sum{f_i \times x_i})}{N}=\dfrac{528}{66}=8$$
Now deviations $$f_i \times |x_i-u|$$ are,
$$30,24,15,25,24,20$$.
$$\therefore MD(u)= \dfrac{(\sum{f_i \times |x_i-u|})}{N}=\dfrac{138}{66}=2.09$$
Thus, $$MD(u)=2.09$$
Ans- Option $$C$$.
Question 4
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Directions For Questions

Factory $$A$$ $$B$$
Number of Workers $$4000$$ $$5000$$
Mean Wages $$3500$$ $$3500$$
Variance in wages $$64$$ $$81$$

...view full instructions

Find the Coefficient of Variation of Factory $$A$$.

A
$$0.22857 \%$$

B
$$0.25758 \%$$

C
$$0.39462 \%$$

D
$$0.82547 \%$$

Solution

Coefficient of Variation, $$C.V=\dfrac{S.D}{Mean} \times 100 \%$$
So, $$C.V_A=\dfrac{S.D_A}{Mean_A} \times 100 \%$$

$$\therefore C.V_A=\dfrac{\sqrt {64}}{3500} \times 100 \%$$.
$$\therefore C.V_A=0.22857 \%$$.
Ans-Option $$A$$.
Question 5
1 / -0

Find the Standard Deviation of the following data:
$$5,9,8,12,6,10,6,8$$

A
$$2.14$$

B
$$2.16$$

C
$$2.15$$

D
$$2.17$$

Solution

Here $$n=8$$.
Mean, $$u=\dfrac{\sum x_i}{n}=\dfrac{64}{8}=8$$
Value of Deviations $$(x_i-u)$$ are
$$-3,1,0,4,-2,2,-2,0$$
Variance, $$\sigma ^2=\dfrac{\sum(x_i-u)^2}{n}\\=\dfrac{(-3-8)^2-(1-8)^2-(0-8)^2-(4-8)^2-(-2-8)^2-(2-8)^2-(-2-8)^2-(0-8)^2}{8}\\=\dfrac{38}{8}=4.75$$.
Standard Deviation, $$S.D=\sqrt{\sigma ^2}$$
$$\therefore S.D=\sqrt{4.75}=2.17$$
Ans- Option $$D$$.
Question 6
1 / -0

Variance remains unchanged by change of

A
scale

B
origin

C
both

D
none of these

Solution

Variance will be changed if scale changes or both scale and origin changes
$$*$$ Variance won't be effected by change of origin.
Question 7
1 / -0

Standard deviation is calculated from the Harmonic Mean (HM).

A
Always

B
Sometimes

C
Never

D
None of these

Solution

Standard deviation is calculated from mean $$i.e$$ arithmetic mean.
It never be calculated from harmonic mean.
Question 8
1 / -0

Directions For Questions

Factory $$A$$ $$B$$
Number of Workers $$4000$$ $$5000$$
Mean Wages $$3500$$ $$3500$$
Variance in wages $$64$$ $$81$$

...view full instructions

Find the Coefficient of Variation for Factory $$B$$:

A
$$0.15555 \%$$

B
$$0.25714 \%$$

C
$$0.36934 \%$$

D
$$0.42548 \%$$

Solution

Coefficient of Variation, $$C.V=\dfrac{\text{S.D}}{\text{Mean}} \times 100 \%$$
So, $$C.V_B=\dfrac{{S.D_B}}{{Mean_B}} \times 100 \%$$
Therefore, $$C.V_B=\dfrac{\sqrt {81}}{3500} \times 100 \%$$
$$\Rightarrow C.V_A=0.25714 \%$$.
Question 9
1 / -0

The formula for the coefficient of range is $$\dfrac{\text{Range}}{a+b}$$. Here, $$a$$ and $$b$$ denote:

A
the mean and median of the data set

B
the maximum and the minimum value of the data set

C
the mean and mode value of the data set

D
the minimum and mean value of the data set

Solution

Range is the difference between the maximum value and the minimum value of the data set.

Let $$a$$ be the maximum value of the data set and
$$b$$ be the minimum value of the data set

Therefore, $$range = a-b$$

Coefficient of range is the relative measure of the dispersion.

It is given by $$\text{coefficient of range}=\dfrac{a-b}{a+b}=\dfrac{range}{a+b}$$
Question 10
1 / -0

The variance of $$10, 10, 10, 10, 10$$, is

A
$$10$$

B
$$\sqrt {10}$$

C
$$0$$

D
$$5$$

Solution

Since we know that if all the data items of a distribution are same. Then, the variance of items is 0.
Here, all the data items are same and equal to 10.
Hence, variance is 0.
Option C is correct.

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Re-Attempt Weekly Quiz Competition

$$x_i$$	$$3$$	$$5$$	$$7$$	$$9$$	$$11$$	$$13$$
$$f_i$$	$$6$$	$$8$$	$$15$$	$$25$$	$$8$$	$$4$$

Factory	$$A$$	$$B$$
Number of Workers	$$4000$$	$$5000$$
Mean Wages	$$3500$$	$$3500$$
Variance in wages	$$64$$	$$81$$

Statistics Test - 19

Result

Statistics Test - 19

Score

-

Rank

-

SHARING IS CARING

Question 1

$$155$$

$$124$$

$$177$$

$$144$$

Solution

Question 2

$$4.765$$

$$4.750$$

$$4.450$$

$$4.420$$

Solution

Question 3

$$2.1$$

$$2.25$$

$$2.09$$

$$2.71$$

Solution

Question 4

$$0.22857 \%$$

$$0.25758 \%$$

$$0.39462 \%$$

$$0.82547 \%$$

Solution

Question 5

$$2.14$$

$$2.16$$

$$2.15$$

$$2.17$$

Solution

Question 6

scale

origin

both

none of these

Solution

Question 7

Always

Sometimes

Never

None of these

Solution

Question 8

$$0.15555 \%$$

$$0.25714 \%$$

$$0.36934 \%$$

$$0.42548 \%$$

Solution

Question 9

the mean and median of the data set

the maximum and the minimum value of the data set

the mean and mode value of the data set

the minimum and mean value of the data set

Solution

Question 10

$$10$$

$$\sqrt {10}$$

$$0$$

$$5$$

Solution

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