Measures of Central Tendency Test

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Measures of Central Tendency Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Determine which type of variable is best to measure the central tendency of mode?

A
nominal

B
ratio

C
interval

D
ordinal

Solution

Nominal is best to measure the central tendency of mode.
The mode can be very useful for dealing with nominal data. For example, if a sandwich shop sells $$10$$ different types of sandwiches, the mode would represent the most popular sandwich.
Question 2
1 / -0

What is the best measure of central tendency for the following diagram?

A
mode

B
mean

C
median

D
range

Solution

Normal distribution of data is the best measure of central tendency for mean.
Here, the diagram shows the normal distribution of data.
Question 3
1 / -0

In which quartile, $$75\%$$ of observations are less than $$Q_3$$ and $$25\%$$ are larger?

A
lower

B
upper

C
middle

D
$$Q_3$$

Solution

In upper quartile, $$75\%$$ of observations are less than $$Q_3$$ and $$25\%$$ are larger.
Example: $$2, 5, 5, 6, 8, 10, 11$$
Here the median is the middle number $$= 6$$
So, the upper quartile is the median of the upper half of the data.
Then, the upper quartile of the first half will be which is $$75\%$$ of the given data less than $$Q_3$$: $$8, 10, 11$$
So, the remaining $$25\%$$ numbers can be considered as larger.
Question 4
1 / -0

______ is called as half of the difference between upper and lower quartiles.

A
Standard deviation

B
Mean deviation

C
Quartile deviation

D
Interquartile range

Solution

Quartile deviation is called as half of the difference between upper and lower quartiles.
Question 5
1 / -0

The notation used for second quartile is

A
$$Q_3$$

B
$$Q_1$$

C
$$Q_2$$

D
$$Q_4$$

Solution

The notation used for second quartile is $$Q_2$$
Question 6
1 / -0

Which type of variable is best to measure the central tendency of median?

A
nominal

B
ratio

C
interval

D
ordinal

Solution

Ordinal is best to measure the central tendency of median.
Example: data set $$= {2, 3, 4, 5, 6, 7, 8}$$
In the ordinal number of data set, median is the middle number, which is $$5$$.
Question 7
1 / -0

What is the best measure of central tendency for the given diagram?

A
mode

B
mean

C
median

D
range

Solution

The diagram shows the distribution is right skewed, so median is the best measure of central tendency.
Question 8
1 / -0

In which distribution, measure of central tendency is equal?

A
left skew

B
right skew

C
normal

D
all the above

Solution

In normal distribution, measure of central tendency is equal.
Example:
Question 9
1 / -0

Find the average of the expressions $$2x+4, 5x-1$$ and $$-x+3$$.

A
$$x+2$$

B
$$x-2$$

C
$$2x+2$$

D
$$2x-2$$

Solution

Average of the expression $$=$$ $$\dfrac{sum \quad of \quad expression }{total \quad no. \quad of \quad expressions}$$
$$\Rightarrow \dfrac{2x+4+5x-1-x+3}{3}$$
$$\Rightarrow \dfrac{6x+6}{3}$$
$$\Rightarrow \dfrac{3(2x+2)}{3}=2x+2$$
Question 10
1 / -0

$$12-n, 12, 12+n$$
What is the average (arithmetic mean) of the $$3$$ quantities in the list above?

A
$$4$$

B
$$12$$

C
$$18$$

D
$$4+\dfrac{n}{3}$$

E
$$12+\dfrac{n}{3}$$

Solution

Given $$3$$ Quantities: $$12$$ $$-$$ $$n$$, $$12$$, $$12$$ $$+$$ $$n$$

Average of the above $$3$$ Quantities $$=$$ $$\dfrac {\text{Sum of the above}\: 3\: \text{Quantities}} {\text{Number of Quantities}} $$

$$=$$ $$\dfrac { 12 \space - \space n \space + \space 12 \space + \space 12 \space + \space n }{3}$$

$$=$$ $$\dfrac {12 \times 3}{3}$$

$$=$$ $$12$$

Therefore, average of the Quantities listed above is $$12$$.

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Re-Attempt Weekly Quiz Competition

Measures of Central Tendency Test - 18

Result

Measures of Central Tendency Test - 18

Score

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SHARING IS CARING

Question 1

nominal

ratio

interval

ordinal

Solution

Question 2

mode

mean

median

range

Solution

Question 3

lower

upper

middle

$$Q_3$$

Solution

Question 4

Standard deviation

Mean deviation

Quartile deviation

Interquartile range

Solution

Question 5

$$Q_3$$

$$Q_1$$

$$Q_2$$

$$Q_4$$

Solution

Question 6

nominal

ratio

interval

ordinal

Solution

Question 7

mode

mean

median

range

Solution

Question 8

left skew

right skew

normal

all the above

Solution

Question 9

$$x+2$$

$$x-2$$

$$2x+2$$

$$2x-2$$

Solution

Question 10

$$4$$

$$12$$

$$18$$

$$4+\dfrac{n}{3}$$

$$12+\dfrac{n}{3}$$

Solution

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