Statistics Test

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Statistics Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is not the measure of dispersion.

A
Quartile Deviation

B
Range

C
Mean Deviation

D
None of these

Solution

Measure of dispersion is the extent to which the distribution is stretched or squeezed.

The common measures of dispersion are standard deviation, variance, interquartile range , mean deviation.
Question 2
1 / -0

Directions For Questions

As median divides an arranged sense into two equal parts, in similar way quartile divides an arranged series in $$4$$ equal part. For ungrouped frequency distribution formula of finding $$i^{th}$$ quartile $$=Q_i=\left\{i\cdot \left(\displaystyle\frac{N+1}{4}\right)\right\}^{th}$$ term, $$i=1, 2, 3$$.
Quartile deviation: half of difference between upper quartile & lower quartile.
$$\Rightarrow$$ Quartile deviation(Q.D.)$$=\displaystyle\frac{1}{2}(Q_3-Q_1)$$
$$\Rightarrow$$ Coefficient of quartile $$=\displaystyle\frac{Q_3-Q_1}{Q_3+Q_1}$$.

...view full instructions

Coefficient of quartile deviation of numbers $$6, 8, 9, 10, 11, 12, 14$$ is?

A
$$1/5$$

B
$$1/10$$

C
$$2/5$$

D
$$1/4$$

Solution

Arranging given numbers in ascending order,
$$6,8,9,10,11,12,14$$
Number of observation $$(N)=7$$
$$Q_i=\left\{i\left(\dfrac{N+1}{4}\right)\right\}^{th}term$$

$$Q_1=\left\{1.\left(\dfrac{7+1}{4}\right)\right\}^{th}term=2^{nd}term$$
$$2^{nd}term=8$$
$$\therefore$$ $$Q_1=8$$

$$Q_3=\left\{3.\left(\dfrac{7+1}{4}\right)\right\}^{th}term=6^{th}term$$
$$6^{th}term=12$$
$$\therefore$$ $$Q_3=12$$

$$\Rightarrow$$ Coefficient of quartile $$=\dfrac{Q_3-Q_1}{Q_3+Q_1}$$

$$=\dfrac{12-8}{12+8}$$

$$=\dfrac{4}{20}$$

$$=\dfrac{1}{5}$$
Question 3
1 / -0

The average marks of $$10$$ students in a class was $$60$$ with standard deviation $$4$$. While the average marks of other $$10$$ students was $$40$$ with a standard deviation $$6$$. If all the $$20$$ students are taken together, their standard deviation will be.

A
$$5.0$$

B
$$7.5$$

C
$$9.8$$

D
$$11.5$$

Solution

Here,
$$n_1=10,\overline{x}_1=60$$ and $$\sigma_1=4$$
$$\therefore$$ $$\sum x_i=60\times 10=600$$
Now, $$n_2=10,\overline{x}_2=40$$ and $$\sigma_2=6$$
$$\therefore$$ $$\sum x_i=10\times 40=400$$
$$\Rightarrow$$ Total marks of $$20$$ students $$(\sum_{i=1}^{20} x)=400+600=1000$$
$$\Rightarrow$$ $$\overline{x}=\dfrac{1000}{20}=50$$

Now, $$\sigma_1^2=(4)^2$$
$$\Rightarrow$$ $$\dfrac{1}{n_1}\sum_{i=1}^{10}x_i^2-(\overline{x_1})^2=16$$
$$\Rightarrow$$ $$\sum_{i=1}^{10}x_i^2=n_1(16+(\overline{x_1})^2)$$
$$=10(16+3600)$$
$$\Rightarrow$$ $$\sum_{i=1}^{10}x_i^2=36160$$

Now, $$\sigma_2^2=(6)^2$$
$$\Rightarrow$$ $$\dfrac{1}{n_2}\sum_{i=11}^{20}x_i^2-(\overline{x_2})^2=36$$

$$\Rightarrow$$ $$\sum_{i=11}^{20}x_i^2=(36+(\overline{x_2})^2)n_2$$
$$=(36+1600)10$$
$$\Rightarrow$$ $$\sum_{i=11}^{20}x_i^2=16360$$
Now, required standard deviation $$(\sigma)=\sqrt{\dfrac{1}{n}\sum x_i^2-\overline{x}^2}$$

$$=\sqrt{\dfrac{1}{20}(36160+16360)-(50)^2}$$
$$=\sqrt{2626-2500}$$
$$=\sqrt{126}$$
$$=11.2$$
Question 4
1 / -0

Find the coefficient of range for the data $$43,24,38,56,22,39,45$$

A
$$0124$$

B
$$0.212$$

C
$$0.236$$

D
$$0.436$$

Solution

Given data is $$43, 24, 38, 56, 2, 39,45$$.
The largest value of data is $$x_m=56$$
The smallest value of data is $$x_0=22$$
Coefficient of data $$=\dfrac{56-22}{56+22}=\dfrac{34}{78}=0.4359\approx 0.436$$
Hence, option D is correct.
Question 5
1 / -0

If $$b_{i} = 1 - a_{i}, na = \displaystyle \sum_{i = 1}^{n} a_{i}, nb = \displaystyle \sum_{i = 1}^{n}b$$, then $$\displaystyle \sum_{i = 1}^{n}a_{i}b_{i} + \displaystyle \sum_{i = 1}^{n} (a_{i} - a)^{2} =$$

A
$$ab$$

B
$$-nab$$

C
$$(n + 1)ab$$

D
$$nab$$

Solution
Question 6
1 / -0

The following are the wages of 8 workers in a factory. Find the range and coefficient of range. Wages are in dollars: 1400, 1450, 1520, 1380, 1485, 1495, 1575, 1440.

A
$$0.0231$$

B
$$0.03112$$

C
$$0.66$$

D
$$0.02314$$

Solution

The largest value of data is $$x_m=1575$$
The smallest value of data is $$x_0=1380$$
Range$$=x_m-x_0=1575-1380=195$$

Coefficient of data$$=\dfrac{1575-1380}{1575+1380}=\dfrac{195}{2955}=0.0659\approx 0.66$$
Question 7
1 / -0

Find the coefficient of range for the given data
$$59,46,30,23,27,40,52,35,29$$

A
$$0.46$$

B
$$0.44$$

C
$$0.56$$

D
$$0.124$$

Solution

Given data is $$59, 46, 30, 23, 27, 40, 52, 35, 29$$.
The largest value of data is $$x_m=59$$
The smallest value of data is $$x_0=23$$
Coefficient of data $$=\dfrac{59-23}{59+23}=\dfrac{36}{82}=0.49\approx 0.44$$
Question 8
1 / -0

Which of the following is correct about measure of dispersion?

A
It does not measure direction of the variation.

B
Dispersion measures the extent to which the items vary from some central value

C
Measures only degree of variation

D
All of the above

Solution

Dispersion measures the extent to which the items vary from some central value. It measures only degree of variation not measure direction of variation.
Question 9
1 / -0

If the coefficient of range is $$0.18$$ and the largest value is $$7.44$$,then the smallest value is?

A
$$3.23$$

B
$$4.15$$

C
$$5.17$$

D
$$5.14$$

Solution

Coefficient of range$$=\dfrac{x_m-x_0}{x_m+x_0}=\dfrac{7.44-x_0}{7.44+x_0}$$
$$0.18(7.44+x_0)=7.44-x_0$$
$$1.18x_0=7.44-7.44\times 0.18$$
$$1.18x_0=6.1008$$
$$x_0=5.17016\approx 5.17$$
Question 10
1 / -0

The weight in Kg of 13 students in a class are $$42.5,47.5,48.6,50.5,49,46.2,49.8,45.8,43.2,48,44.7,46.9,42.4$$.Find the coefficient of range.

A
$$0.077$$

B
$$0.213$$

C
$$0.0803$$

D
$$0.093$$

Solution

The largest value of data is $$x_m=49.8$$
The smallest value of data is $$x_0=42.4$$
Coefficient of data$$=\dfrac{49.8-42.4}{49.8+42.4}=\dfrac{7.4}{92.2}=0.08026\approx 0.0803$$

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Re-Attempt Weekly Quiz Competition

Statistics Test - 38

Result

Statistics Test - 38

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SHARING IS CARING

Question 1

Quartile Deviation

Range

Mean Deviation

None of these

Solution

Question 2

$$1/5$$

$$1/10$$

$$2/5$$

$$1/4$$

Solution

Question 3

$$5.0$$

$$7.5$$

$$9.8$$

$$11.5$$

Solution

Question 4

$$0124$$

$$0.212$$

$$0.236$$

$$0.436$$

Solution

Question 5

$$ab$$

$$-nab$$

$$(n + 1)ab$$

$$nab$$

Solution

Question 6

$$0.0231$$

$$0.03112$$

$$0.66$$

$$0.02314$$

Solution

Question 7

$$0.46$$

$$0.44$$

$$0.56$$

$$0.124$$

Solution

Question 8

It does not measure direction of the variation.

Dispersion measures the extent to which the items vary from some central value

Measures only degree of variation

All of the above

Solution

Question 9

$$3.23$$

$$4.15$$

$$5.17$$

$$5.14$$

Solution

Question 10

$$0.077$$

$$0.213$$

$$0.0803$$

$$0.093$$

Solution

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