Descriptive Statistics Test 15

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Descriptive Statistics Test 15

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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

Which one is correct?
Statement 1:Positional measure of dispersion describes about the position that a particular data value has within a data set.
Statement 2:Quartiles and percentiles are positional measure of dispersion.

A
$$1$$ only

B
$$2$$ only

C
$$1$$ and $$2$$ both

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

Solution

Statement 1: is correct because positional measure of dispersion describes about the position that a particular data value has within a data set.
Statement 2:is correct because quartiles and percentiles are positional measure of dispersion.
Question 3
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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 4
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.
Question 5
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

Quartile deviation of the following numbers $$10, 8, 12, 11, 14, 9, 6$$ is?

A
$$2$$

B
$$10$$

C
$$1/2$$

D
$$1$$

Solution

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

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

$$Q_3=\left\{3.\left(\dfrac{7+1}{4}\right)\right\}^{th}term=6^{th}term$$
$$6^{th}term=12$$
$$\therefore$$ $$Q_3=12$$
$$\therefore$$ Quartile deviation $$=\dfrac{1}{2}(Q_3-Q_1)$$

$$=\dfrac{1}{2}(12-8)$$

$$=\dfrac{4}{2}$$

$$=2$$
Question 6
1 / -0

Quartile Deviation =

A
Half of the Inter-Quartile Range

B
[ Q(3) - Q(1) ] / 2

C
Both A and B

D
Q(3) - Q(1)
Question 7
1 / -0

Inter Quartile Range =

A
Difference between the upper and lower quartiles

B
Q(3) - Q(1)

C
Both A and B

D
Q(2)-Q(1)
Question 8
1 / -0

Fill the alternative given in the bracket:
Systematic arrangement of data in table and row is called _________.

A
tabulation

B
graph

C
caption

D
pie chart
Question 9
1 / -0

In a tabular presentation, data is presented in ______ and ______.

A
rows and columns

B
lines and graphs

C
texts and paragraphs

D
A and B

Solution

The process of classifying data into tabular form is called "Tabulation".
A table is a symmetric arrangement of data in rows and columns. Rows are horizontal arrangements and columns are vertical arrangements.
Question 10
1 / -0

Which of the following is true with respect to range?

A
Higher value of Range implies higher dispersion and vice-versa

B
Range is unduly affected by extreme values.

C
It is not based on all the values.

D
All of these

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Descriptive Statistics Test 15

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Descriptive Statistics Test 15

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SHARING IS CARING

Question 1

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

$$t + 5$$

$$t$$

$$xyz$$

Solution

Question 2

$$1$$ only

$$2$$ only

$$1$$ and $$2$$ both

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

Solution

Question 3

Mean

Median

Mode

Variance

Solution

Question 4

$$10$$

$$11$$

$$12$$

$$13$$

Solution

Question 5

$$2$$

$$10$$

$$1/2$$

$$1$$

Solution

Question 6

Half of the Inter-Quartile Range

[ Q(3) - Q(1) ] / 2

Both A and B

Q(3) - Q(1)

Question 7

Difference between the upper and lower quartiles

Q(3) - Q(1)

Both A and B

Q(2)-Q(1)

Question 8

tabulation

graph

caption

pie chart

Question 9

rows and columns

lines and graphs

texts and paragraphs

A and B

Solution

Question 10

Higher value of Range implies higher dispersion and vice-versa

Range is unduly affected by extreme values.

It is not based on all the values.

All of these

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