Statistics Test

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Statistics Test - 40

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Weekly Quiz Competition

Question 1
1 / -0

The mean is_____________________.

A
the statistical or arithmetic average

B
the middlemost score

C
the most frequently occurring score

D
the best representation for every set of data

Solution

Mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class.
i.e.
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$
Question 2
1 / -0

Consider the following statements:
(1) Mean is independent of change in scale and change in origin
(2) Variance is independent of change in scale but not in origin
Which of the above statements is/are correct?

A
1 only

B
2 only

C
Both 1 and 2

D
Neither 1 nor 2

Solution

Mean changes with changes in origin as if $$x$$ is added to all the value, $$nx$$ is added to total value and then, divided by $$n$$ to get an addition of $$x$$.
Variance is independent to the choice of origin as variance is $$(a-\overline{a})^2$$ which negates the addition in observation value and the mean as shown above.
Hence, answer is neither 1 nor 2.
Question 3
1 / -0

The arithmetic mean between $$\cfrac { x+a }{ x } $$ and $$\cfrac { x-a }{ x } $$ when $$x\ne 0$$, is (the symbol $$\ne$$ means "not equal to"):

A
$$2$$, if $$a\ne 0$$

B
$$1$$

C
$$1$$, only if $$a=0$$

D
$$\dfrac {a}{x}$$

E
$$x$$

Solution

The arithmetic mean between two quantities is given by,
A.M.=$$\dfrac{\dfrac{x+a}{x}+\dfrac{x-a}{x}}{2}$$
=$$\dfrac{x+a+x-a}{2x}$$
=$$\dfrac{2x}{2x}$$
=1
Hence A.M.=1
Question 4
1 / -0

Consider the following statements:
$$1.$$ Variance is unaffected by change of origin and change of scale.
$$2.$$ Coefficient of variance is independent of the unit of observations.
Which of the statements given above is/ are correct?

A
$$1$$ only

B
$$2$$ only

C
Both $$1$$ and $$2$$

D
Neither $$1$$ nor $$2$$

Solution

Variance is independent of change of origin as the change in origin is uniformly added to all the values and hence the mean also and hence, when $$(x-\overline{x})^2$$ is calculated, it remains unaffected. But, change of scale alters all values unevenly and hence, variation changes.
The coefficient of variance is standard deviation by mean which doesn't depend on the unit of observation.
So, Statement 1 is incorrect Statement 2 is correct
Question 5
1 / -0

The average (arithmetic mean) of a set of seven numbers is $$8$$. When an eighth number is added to the set, the average of the eight numbers is still $$8$$. What number was added to the set?

A
$$6$$

B
$$7$$

C
$$8$$

D
$$9$$
Question 6
1 / -0

Consider the following statements:
$$1.$$ Coefficient of variation depends on the unit of measurement of the variable.
$$2.$$ Range is a measure of dispersion.
$$3.$$ Mean deviation is least when measured about median.
Which of the above statements are correct?

A
$$1$$ and $$2$$ only

B
$$2$$ and $$3$$ only

C
$$1$$ and $$3$$ only

D
$$1, 2$$ and $$3$$

Solution

Unit of measurement change changes the mean as well as standard deviation and hence the coefficient of variation.
Range implies how much the values are spread or dispersed.
Mean derivation is least when measured about mean, therefore statement 3 is wrong.
Statement 1 and statement 2 are correct.
Question 7
1 / -0

If the mode of five observations, in order, $$0, 2, 3, m, 5$$ is $$3$$ then $$m =$$ _______.

A
$$5$$

B
$$2$$

C
$$3$$

D
$$0$$

Solution

If the mode of five observation, in order, $$0, 2, 3, m, 5$$ is $$3$$,
then $$m = 3$$.
Question 8
1 / -0

Find out the coefficient of range for the following prices of shirts in a shop.
Rupees
150
250
100
500
175
450
300
280

A
1.25

B
0.666

C
0.333

D
0.30

Solution

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Therefore, it is the most affected measures of dispersion by the extreme values of the series.
Range = H - L
In the given series, H= 500 and L= 100
Range = 500-100 = 400.
Coefficient of range is found by dividing the range with the sum of highest and lowest value of the series.
Coefficient of range (CR) = R/ (H+L)
=400 / (500+100)

= 400/ 600 = 0.666
Question 9
1 / -0

Find out the range for the following prices of shirts in a shop.
Rupees
150
250
100
500
175
450
300
280

A
Rs. 400

B
Rs. 500

C
Rs. 350

D
Rs. 100

Solution

Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Therefore, it is the most affected measures of dispersion by the extreme values of the series.

Range = H - L

In the given series, H= 500 and L= 100

Range = 500-100 = 400.
Question 10
1 / -0

Let mean of $$100$$ data points be $$55$$ and variance be $$16$$ . Now if every data point is increased by $$2$$ units, then the sum of mean and standard deviation of new data point will be:

A
$$71$$

B
$$59$$

C
$$63$$

D
$$61$$

Solution

As the 2 units are added to every point on the data , there will be no change in the standard deviation .But mean will raise by 2units
Hence new mean = 57
Given Variance=16
Standard deviation = $$\sqrt{variance}=\sqrt{16}=4$$
Sum of mean and standard deviation = $$57+4=61$$ units

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Statistics Test - 40

Result

Statistics Test - 40

Score

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Rank

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SHARING IS CARING

Question 1

the statistical or arithmetic average

the middlemost score

the most frequently occurring score

the best representation for every set of data

Solution

Question 2

1 only

2 only

Both 1 and 2

Neither 1 nor 2

Solution

Question 3

$$2$$, if $$a\ne 0$$

$$1$$

$$1$$, only if $$a=0$$

$$\dfrac {a}{x}$$

$$x$$

Solution

Question 4

$$1$$ only

$$2$$ only

Both $$1$$ and $$2$$

Neither $$1$$ nor $$2$$

Solution

Question 5

$$6$$

$$7$$

$$8$$

$$9$$

Question 6

$$1$$ and $$2$$ only

$$2$$ and $$3$$ only

$$1$$ and $$3$$ only

$$1, 2$$ and $$3$$

Solution

Question 7

$$5$$

$$2$$

$$3$$

$$0$$

Solution

Question 8

1.25

0.666

0.333

0.30

Solution

Question 9

Rs. 400

Rs. 500

Rs. 350

Rs. 100

Solution

Question 10

$$71$$

$$59$$

$$63$$

$$61$$

Solution

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