Measures of Central Tendency Test

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Measures of Central Tendency Test - 12

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Question 1
1 / -0

The weights (in $$kg$$) of $$13$$ students are given below:
$$44$$, $$42$$, $$43$$, $$46$$, $$52$$, $$39$$, $$40$$, $$42$$, $$41$$, $$47$$, $$49$$, $$38$$, $$50$$ Calculate the median weight

A
$$58\: kg$$

B
$$43\: kg$$

C
$$36\: kg$$

D
$$31\:kg$$

Solution

Weight of 13 students is:
$$44$$, $$42$$, $$43$$, $$46$$, $$52$$, $$39$$, $$40$$, $$42$$, $$41$$, $$47$$, $$49$$, $$38$$, $$50$$
Arranging the weights in ascending order:
$$38, 39, 40, 41,42, 42, 43, 44, 46,47, 49, 50, 52$$
Since, the number of students is $$13$$, the median will be the middle most observation,
here, it is $$7^{th}$$ term i.e. $$43$$
Question 2
1 / -0

Calculate the mode for the following data:
$$20$$, $$18$$, $$20$$, $$16$$, $$15$$, $$23$$, $$16$$, $$17$$, $$15$$, $$16$$

A
$$23$$

B
$$15$$

C
$$20$$

D
$$16$$

Solution

From the given observations:
$$20$$, $$18$$, $$20$$, $$16$$, $$15$$, $$23$$, $$16$$, $$17$$, $$15$$, $$16$$
Here, $$16$$ is the most frequent observation, hence it is the mode of the series.
Question 3
1 / -0

Mode of the observations $$5, 7, 2, 8, 5, 5, 8, 2, 5, 8, 7, 6$$ is

A
$$7$$

B
$$6$$

C
$$6.5$$

D
$$5$$

Solution

For the given data: $$5$$, $$7$$, $$2$$, $$8$$, $$5$$, $$5$$, $$8$$, $$2$$, $$5$$, $$8$$, $$7$$, $$6$$
$$5$$ occurs most frequently. hence, the mode is $$5$$
Question 4
1 / -0

Mean of the first six even numbers is

A
$$7$$

B
$$5$$

C
$$3$$

D
$$1$$

Solution

Formula used:
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$

Apply the above formula, we get
Mean$$=\displaystyle \frac{2+4+6+8+10+12}{6}$$
= $$\displaystyle \frac{42}{6}=7$$
Question 5
1 / -0

Find the median of each of the following data:
$$(i)$$ $$7$$, $$10$$, $$5$$, $$20$$, $$18$$, $$25$$, $$17$$
$$(ii)$$ $$3$$, $$5$$, $$9$$, $$2$$, $$8$$, $$7$$, $$6$$, $$7$$, $$4$$
$$(iii)$$ $$37$$, $$42$$, $$31$$, $$46$$, $$25$$, $$27$$, $$30$$, $$32$$, $$41$$

A
$$(i)$$ $$18$$
$$(ii)$$ $$4$$
$$(iii)$$ $$20$$

B
$$(i)$$ $$5$$
$$(ii)$$ $$36$$
$$(iii)$$ $$13$$

C
$$(i)$$ $$17$$
$$(ii)$$ $$6$$
$$(iii)$$ $$32$$

D
$$(i)$$ $$9$$
$$(ii)$$ $$29$$
$$(iii)$$ $$30$$

Solution

$$(i)$$ By arranging the given no's in increasing order, we get:
    $$ 5,7,10,17,18,20,25 $$
    Total terms $$= 7$$
since, the middle most term is $$ 4^{th} $$.
$$\therefore $$ value of median is $$17$$
$$(ii)$$ By arranging the given no's in increasing order, we get:
   $$ 2,3,4,5,6,7,7,8,9 $$
   Total terms $$= 9$$
   since, the middle most term is $$ 5^{th} $$.
   $$\therefore $$ value of median is $$6$$
$$(iii)$$ By arranging the given no's in increasing order, we get:
   $$ 25,27,30,31,32,37,41,42,46 $$
   Total terms $$= 9$$
   since, the middle most term is $$ 5^{th} $$.
   $$\therefore $$ value of median is $$32$$
Question 6
1 / -0

Find the mode for the following: $$36$$, $$32$$, $$31$$, $$31$$, $$29$$, $$31$$, $$30$$, $$32$$, $$40$$, $$46$$, $$31$$, $$32$$, $$35$$, $$37$$, $$40$$. If one observation $$31$$ is replaced by $$32$$, will the modal value change? If yes, find it

A
$$31$$, Yes, $$32$$

B
$$33$$, No

C
$$37$$, Yes, $$30$$

D
$$32$$, No

Solution

By arranging the given data in increasing order, we get,
$$ 29,30,31,31,31,31,32,32,32,35,36,37,40,40,46 $$
value that occurs most frequently is $$31$$
$$\therefore $$ Mode $$= 31$$
if one $$31$$ is replaced by $$32$$ then the arranging data is:
$$ 29,30,32,32,32,32,32,32,32,35,36,37,40,40,46 $$
Now the value that occurs most frequently is $$32$$
so, now modal value is change. i.e $$32$$
Question 7
1 / -0

A variate takes $$11$$ values which are arranged in ascending order of their magnitudes It is found that $$4$$th, $$6$$th and $$8$$th observations are $$8$$, $$6$$ and $$4$$ respectively What is the median of the distribution?

A
$$4$$

B
$$6$$

C
$$8$$

D
$$10$$

Solution

Since there are $$11$$ values
median = middle value = $$6^{th}$$ value = $$6$$
Question 8
1 / -0

The runs scored by some players of a cricket team in a one day match are given below:
$$83$$, $$40$$, $$36$$, $$0$$, $$69$$, $$105$$, $$73$$, $$21$$, $$8$$ Find the median runs

A
$$39$$ runs

B
$$52$$ runs

C
$$40$$ runs

D
None of these

Solution

Runs scored by players are:
$$83$$, $$40$$, $$36$$, $$0$$, $$69$$, $$105$$, $$73$$, $$21$$, $$8$$
Arranging them in ascending order:
$$0, 8, 21, 36, 40, 69, 73, 83, 105$$
The number of players are $$9$$, the median will be the middle most number, i.e. $$5^{th}$$ term.
Hence, median is $$40$$ runs
Question 9
1 / -0

The marks obtained by $$10$$ students in a test are:
$$12$$, $$22$$, $$32$$, $$41$$, $$26$$, $$30$$, $$14$$, $$11$$, $$18$$, $$35$$. Find the median marks

A
$$24$$ marks

B
$$28$$ marks

C
$$32$$ marks

D
None of these

Solution

Marks obtained by $$10$$ students in the test:
$$12$$, $$22$$, $$32$$, $$41$$, $$26$$, $$30$$, $$14$$, $$11$$, $$18$$, $$35$$
Arranging the marks in ascending order:
$$11, 12, 14, 18, 22, 26, 30, 32, 35, 41$$
Since, the number of students are $$10$$, median will be the mean of two middle terms
Median $$=$$ mean of $$5^{th}$$ term and $$6^{th}$$ term
Median $$= \dfrac{22 + 26}{2}$$
Median $$= 24$$ marks
Question 10
1 / -0

The arithmetic mean of first five natural numbers is

A
$$3$$

B
$$4$$

C
$$5$$

D
$$6$$

Solution

Formula used:
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$

Apply the above formula, we get
$$\displaystyle AM=\frac{1+2+3+4+5}{5}=3$$

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Re-Attempt Weekly Quiz Competition

Measures of Central Tendency Test - 12

Result

Measures of Central Tendency Test - 12

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Question 1

$$58\: kg$$

$$43\: kg$$

$$36\: kg$$

$$31\:kg$$

Solution

Question 2

$$23$$

$$15$$

$$20$$

$$16$$

Solution

Question 3

$$7$$

$$6$$

$$6.5$$

$$5$$

Solution

Question 4

$$7$$

$$5$$

$$3$$

$$1$$

Solution

Question 5

$$(i)$$ $$18$$$$(ii)$$ $$4$$$$(iii)$$ $$20$$

$$(i)$$ $$5$$$$(ii)$$ $$36$$$$(iii)$$ $$13$$

$$(i)$$ $$17$$$$(ii)$$ $$6$$$$(iii)$$ $$32$$

$$(i)$$ $$9$$$$(ii)$$ $$29$$$$(iii)$$ $$30$$

Solution

Question 6

$$31$$, Yes, $$32$$

$$33$$, No

$$37$$, Yes, $$30$$

$$32$$, No

Solution

Question 7

$$4$$

$$6$$

$$8$$

$$10$$

Solution

Question 8

$$39$$ runs

$$52$$ runs

$$40$$ runs

None of these

Solution

Question 9

$$24$$ marks

$$28$$ marks

$$32$$ marks

None of these

Solution

Question 10

$$3$$

$$4$$

$$5$$

$$6$$

Solution

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$$(i)$$ $$18$$
$$(ii)$$ $$4$$
$$(iii)$$ $$20$$

$$(i)$$ $$5$$
$$(ii)$$ $$36$$
$$(iii)$$ $$13$$

$$(i)$$ $$17$$
$$(ii)$$ $$6$$
$$(iii)$$ $$32$$

$$(i)$$ $$9$$
$$(ii)$$ $$29$$
$$(iii)$$ $$30$$