Descriptive Statistics Test 13

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Descriptive Statistics Test 13

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Weekly Quiz Competition

Question 1
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Directions For Questions

Study the following bar chart and answer the questions carefully.

...view full instructions

What is the approximate difference between the average sales turnover of all the companies put together between the years 2001 - 2002 and 2002 - 2003?

A
133.45

B
142.48

C
117.6

D
None of these

Solution

The sum of the difference between two years divided by 5.'
Question 2
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Directions For Questions

The following bar chart shows the trends of foreign direct investments(FDI) into India from all over the world.

...view full instructions

What was the ratio of investment in 1997 over the investment in 1992?

A
5.50

B
5.36

C
5.64

D
5.75

Solution

The 1997 figure of investment as a factor of 1992 investment = (31.36/5.70) = 5.50
Question 3
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Find the mean deviation about the mean of the following data:
$$15,17,10,13,7,18,9,6,14,11$$.

A
$$3.1$$

B
$$3.2$$

C
$$3.3$$

D
$$3.4$$

Solution

Let the mean of data be $$u=\dfrac{\sum x_i}{n}=\dfrac {120}{10}=12$$
Calculating the deviation : $$|x_i-u|$$ we get,
$$3,5,-2,1,5,6,3,6,2,1$$.
$$\therefore M.D (u)= \dfrac{\sum{|x_i-u|}}{n}= \dfrac{34}{10}=3.4$$
Thus, $$M.D(u) =3.4$$.
Ans- Option $$D$$
Question 4
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Find odd one out:
Mean, Median, Mode, Variance

A
Mean

B
Median

C
Mode

D
Variance

Solution

Mean, median, mode are the measures of the central tendencies. Therefore, the odd one is the variance.
Question 5
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$${\sigma}^2$$ is known as

A
mean

B
variance

C
Standard deviation

D
quartile deviation

Solution

Variance gives the degree to which the numerical data tend to spread about the value.

Variance is denoted by $$\sigma^2$$

Variance is given by $$\dfrac{\sum x^2}{n}-(\dfrac{\sum x}{n})^2$$

But mean $$\bar x=\dfrac{\sum x}{n}$$

Therefore, variance is $$\dfrac{\sum x^2}{n}-(\bar x)^2$$
Question 6
1 / -0

Find odd man out:
Standard Deviation, Variance, Mean, Quartile deviation.

A
Standard Deviation

B
Variance

C
Mean

D
Quartile deviation

Solution

Standard deviation, variance, quartile deviation gives the dispersion of the data. Therefore the odd one is mean.
Question 7
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Variance can be calculated using:

A
$${\dfrac{\sum x^2}{n}-\left(\dfrac{\sum x}{n}\right)^2}$$

B
$$\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)}{n}\right)}$$

C
$$\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)^2}{n}\right)}$$

D
$$\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)^2}{n}\right)$$

Solution

Variance gives the degree to which the numerical data tend to spread about the value.

Variance is given by $$\dfrac{\sum x^2}{n}-(\dfrac{\sum x}{n})^2$$
Question 8
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Directions For Questions

The following chart shows the production of cars in thousands.

...view full instructions

The ratio of Hindustan Motors production in 2003 - 2004 to Honda's production in 2002 - 2003 is?

A
0.66

B
1.5

C
2

D
None of these

Solution

The required ratio is (9/6) = 1.5.'
Question 9
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Find the variance of first $$10$$ multiples of $$3$$.

A
$$72.65$$

B
$$74.05$$

C
$$74.25$$

D
$$73.85$$

Solution

First $$10$$ multiples of $$3$$ are $$3,6,9...30$$.
This is an A.P.
$$sum=\dfrac n2 (a+l)= \dfrac {10}{2} \times (3+30)$$
$$\therefore sum=165$$.
Mean, $$u=\dfrac {sum}{n}=\dfrac{165}{10}$$.
Variance, $$\sigma ^2=\dfrac{\sum(x_i ^2)}{n}-u^2$$.
$$\therefore \sigma ^2=\dfrac{3^2+6^2+...30^2}{10}-{16.5}^2$$.
$$\therefore \sigma ^2=\dfrac{3\times(1^2+2^2+...10^2)}{10}-{16.5}^2$$.
$$\therefore \sigma ^2=\dfrac{9\times 10\times (10+1)\times (2\times 10+1)}{6\times 10}-{16.5}^2$$.
$$\therefore \sigma ^2=346.5-272.25$$
$$\therefore \sigma ^2=74.25$$
Ans-Option $$C$$.
Question 10
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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 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, $$C.V_B=\dfrac{\sqrt {81}}{3500} \times 100 \%$$
$$\Rightarrow C.V_A=0.25714 \%$$.

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

Descriptive Statistics Test 13

Result

Descriptive Statistics Test 13

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Question 1

133.45

142.48

117.6

None of these

Solution

Question 2

5.50

5.36

5.64

5.75

Solution

Question 3

$$3.1$$

$$3.2$$

$$3.3$$

$$3.4$$

Solution

Question 4

Mean

Median

Mode

Variance

Solution

Question 5

mean

variance

Standard deviation

quartile deviation

Solution

Question 6

Standard Deviation

Variance

Mean

Quartile deviation

Solution

Question 7

$${\dfrac{\sum x^2}{n}-\left(\dfrac{\sum x}{n}\right)^2}$$

$$\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)}{n}\right)}$$

$$\sqrt{\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)^2}{n}\right)}$$

$$\dfrac{\sum x^2}{n}-\left(\dfrac{(\sum x)^2}{n}\right)$$

Solution

Question 8

0.66

1.5

2

None of these

Solution

Question 9

$$72.65$$

$$74.05$$

$$74.25$$

$$73.85$$

Solution

Question 10

$$0.15555 \%$$

$$0.25714 \%$$

$$0.36934 \%$$

$$0.42548 \%$$

Solution

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