Measures of Central Tendency Test

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Measures of Central Tendency Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

The average of daily wages for the workers of the two factories combined is
No.of wage earners Factory A 250 Factory B 200
Average daily wage Rs.2.00 Rs.2.50

A
$$2.22$$

B
$$3.15$$

C
$$4.10$$

D
None of these

Solution

Average wage$$ = \cfrac{x_1w_1+x_2w_2}{w_1+w_2}$$

$$=\cfrac{250\times 2+200\times 2.5}{250+200}$$

$$=\cfrac{1000}{450}=2.22$$
Question 2
1 / -0

Find the median of the given data.
$$30, 32, 24, 34, 26, 28, 30, 35, 33, 25$$

A
$$32$$

B
$$26$$

C
$$30$$

D
$$25$$

Solution

Arranging the data in ascending order:
$$24,25,26,28,30,30,32,33,34,35$$
Mean $$=\dfrac {\text { sum of all numbers} }{ \text {count of all numbers }} = \dfrac { 24+25+26+28+30+30+32+33+34+35}{10} =\dfrac { 297 }{10 } =29.7 $$
Median of even number of data is the average of the middle two terms that is here the average of $$5^{th}$$ and $$6^{th}$$ terms.
Median$$ =\dfrac { 30+30 }{ 2 } =30
$$
Question 3
1 / -0

Frequency distribution of daily commission received by 100 salesmen is given.
Daily commission (in Rs.) $$100 - 120$$ $$120 - 140$$ $$140 - 160$$ $$160 - 180$$ $$180 - 200$$
No. of salesman $$20$$ $$45$$ $$22$$ $$9$$ $$4$$
Find mean daily commission received by a salesman.

A
$$136.4$$

B
$$140$$

C
$$130$$

D
None of these

Solution

Rs No.of salesman $$x$$ $${ f }_{ x }$$
$$100-120$$ $$ 20$$ $$110$$ $$2200$$
$$120-140 $$ $$ 45$$ $$130$$ $$5850$$
$$140-160$$ $$22$$ $$150$$ $$3300$$
$$160-180$$ $$9$$ $$170$$ $$1530$$
$$180-200$$ $$ 4$$ $$190$$ $$760$$
$$100$$ $$13640$$
$$\bar { x }$$ =$$\cfrac { \sum { fx } }{ \sum { f } } =\cfrac { 13640 }{ 100 } =Rs136.4$$
Question 4
1 / -0

Find the mean of first ten odd natural numbers.

A
$$10$$

B
$$11$$

C
$$12$$

D
None of these

Solution

$${\textbf{Step -1: Listing first 10 odd natural numbers .}}$$

$${\text{First 10 odd natural numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19}}$$

$${\textbf{Step -2: Calculating mean}}$$

$${\text{We know that, mean of n numbers = }}\dfrac{{{\text{Sum of n numbers}}}}{{\text{n}}}$$

$$\therefore {\text{ Mean of first 10 odd natural numbers,}}$$
$${\text{M = }}\dfrac{{{\text{1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19}}}}{{{\text{10}}}}$$

$$ \Rightarrow {\text{ M = }}\dfrac{{{\text{100}}}}{{{\text{10}}}}{\text{ = 10}}$$

$${\textbf{Thus, the mean of first 10 odd natural numbers is 10 .}}$$
Question 5
1 / -0

Find the median of:
$$25, 16, 26, 16, 32, 31, 19, 28$$ and $$35$$.

A
$$25$$

B
$$24$$

C
$$26$$

D
$$28$$

Solution

Arranging the series in ascending order:
$$16, 16, 19, 25, 26, 28, 31, 32, 35$$
The series has $$9$$ terms, the median is the middle term.Hence, $$26$$ is the median of the series.
Question 6
1 / -0

Find the median of:
$$241, 243, 347, 350, 327, 299, 261, 292, 271, 258$$ and $$257.$$

A
$$271$$

B
$$275$$

C
$$276$$

D
$$285$$

Solution

Arrange the series in ascending order:
$$241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350$$
The series has $$11$$ terms. Hence, the median will be the middle term, i.e. $$6^{th}$$ term.
Hence, the median is $$271$$
Question 7
1 / -0

Find the median of the following data.
$$150, 147, 140, 120, 135, 139, 148, 148$$

A
$$140$$

B
$$143.5$$

C
$$148$$

D
$$150$$

Solution

The data points are: $$150, 147, 140, 120, 135, 139, 148, 148$$
Arranging in ascending order: $$120, 135, 139, 140, 147, 148, 148, 150$$
The number of observations are $$8$$. Since, the observations are even, the median will be the mean of $$\cfrac{n}{2}$$ and $$\cfrac{n+2}{2}$$ observations
median $$=$$ mean of $$\cfrac{8}{2}$$ and $$\cfrac{8+2}{2}$$ observations
median $$=$$ mean of 4th and 5th observations
median $$= \cfrac{140+ 147}{2}$$
median $$= 143.5$$
Question 8
1 / -0

Find the median of the data: $$ 35, 48, 92, 76, 64. 52, 51, 63$$ and $$71$$

A
$$71$$

B
$$64$$

C
$$52$$

D
$$48$$

Solution

Arranging the data in ascending order:
$$35,48,51,52,63,64,71,76,92$$
Mean $$=\dfrac {\text { sum of all numbers }}{ \text {count of all numbers }} = \dfrac { 35+48+51+52+63+64+71+76+92 }{ 9 } =\dfrac { 552 }{ 9 } =61.33$$
Since the number of data is odd the median will be the middlemost term.
So, Median $$=63$$ of the numbers would become:
$$ 35,48,52,63,64,66,71,76,92$$
The new Median is $$64$$.
Question 9
1 / -0

The marks obtained by twenty students are given as follows.
$$27, 22, 24, 17, 16, 15, 14, 22, 17, 15, 22, 26, 19, 22, 20, 22, 16, 15, 22, 27$$
Find the modal marks.

A
$$20$$

B
$$22$$

C
$$24$$

D
$$26$$

Solution

Marks obtained by $$20$$ students : $$27, 22, 24, 17, 16, 15, 14, 22, 17, 15, 22, 26, 19, 22, 20, 22, 16, 15, 22, 27$$
Arranging them in ascending order: $$14, 15, 15,15, 16,16, 17, 17, 19, 20, 22, 22, 22, 22, 22, 22, 24, 26, 27, 27$$
$$22$$ occurs $$6$$ and maximum number of times in the data. Hence, $$22$$ is the modal marks.
Question 10
1 / -0

A cricket player scored runs in different matches as follows.
$$36, 41, 57, 89, 105, 103, 17$$. Find the median.

A
$$41$$

B
$$57$$

C
$$89$$

D
$$103$$

Solution

The data points are: $$36, 41, 57, 89, 105, 103, 17$$
Arranging in ascending order: $$17, 36, 41, 57, 89, 103, 105$$
The number of observations are $$7$$. Since, the observations are odd, the median will be the $$\cfrac{n+1}{2}$$ observations
median $$= \cfrac{7+1}{2}$$ observations
median $$= 4^{th}$$ observations
median $$= 57$$

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Re-Attempt Weekly Quiz Competition

No.of wage earners	Factory A 250	Factory B 200
Average daily wage	Rs.2.00	Rs.2.50

Daily commission (in Rs.)	$$100 - 120$$	$$120 - 140$$	$$140 - 160$$	$$160 - 180$$	$$180 - 200$$
No. of salesman	$$20$$	$$45$$	$$22$$	$$9$$	$$4$$

Measures of Central Tendency Test - 10

Result

Measures of Central Tendency Test - 10

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SHARING IS CARING

Question 1

$$2.22$$

$$3.15$$

$$4.10$$

None of these

Solution

Question 2

$$32$$

$$26$$

$$30$$

$$25$$

Solution

Question 3

$$136.4$$

$$140$$

$$130$$

None of these

Solution

Question 4

$$10$$

$$11$$

$$12$$

None of these

Solution

Question 5

$$25$$

$$24$$

$$26$$

$$28$$

Solution

Question 6

$$271$$

$$275$$

$$276$$

$$285$$

Solution

Question 7

$$140$$

$$143.5$$

$$148$$

$$150$$

Solution

Question 8

$$71$$

$$64$$

$$52$$

$$48$$

Solution

Question 9

$$20$$

$$22$$

$$24$$

$$26$$

Solution

Question 10

$$41$$

$$57$$

$$89$$

$$103$$

Solution

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