Measures of Central Tendency Test

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Measures of Central Tendency Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

The median of the first 12 prime numbers is

A
$$12$$

B
$$13$$

C
$$14$$

D
$$15$$

Solution

First 12 prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37
Median$$=\dfrac{13+17}{2}=\dfrac{30}{2}=15$$
Question 2
1 / -0

The numbers 3,5,6 and 4 have frequencies of x x+2, x-8 and x+6 respectively If their mean is 4 then the value of x is

A
$$5$$

B
$$6$$

C
$$7$$

D
$$4$$

Solution

x f fx
3 x 3x
5 x+2 5x+10
6 x-8 6x-48
4 x+6 4x+24
$$\bar x=\dfrac{\sum fx}{n}$$
where n=The sum of the frequency
Given $$\bar x=4$$
$$\therefore \bar 4=\dfrac{18x-14}{4x}$$
$$\Rightarrow 16x=18x-14$$
$$\Rightarrow 16x-14x=-14$$
$$\Rightarrow -2x=-14$$
$$\Rightarrow x=\dfrac{-14}{-2}=7$$
Question 3
1 / -0

A contractor employed 18 labourers at Rs 12 per day 10 labourers at Rs 13.50 per day 5 labourers at Rs 25 per day and 2 labourers at Rs 42 per day The average wage of a laborer per day is

A
$$Rs\ 16$$

B
$$Rs\ 20$$

C
$$Rs\ 24$$

D
$$Rs\ 28$$

Solution

The average wage$$=\dfrac{18\times 12+10\times 13.50+5\times 25+42\times 2}{35}$$
$$\Rightarrow \dfrac {216+135+125+84}{35}=\dfrac{560}{35}=Rs.16$$
Question 4
1 / -0

The mode of the series 2,3,1,2,5,3,2,2,3,5 is

A
5

B
1

C
2

D
3

Solution

2 has highest frequency
Question 5
1 / -0

A data has 25 observations (arranged in descending order) which observations represents the median?

A
$$\displaystyle 13^{th}$$

B
$$\displaystyle 14^{th}$$

C
$$\displaystyle 15^{th}$$

D
none of these

Solution

Number of observations =25
Number of observation are odd then
Median=value of $$\left(\dfrac{n+1}{2}\right)^{th}$$observation
$$\Rightarrow \dfrac{25+1}{2}=\dfrac{26}{2}=13^{th} $$observation
Question 6
1 / -0

A student obtained the following marks percentage in an examination English - 50, Accounts - 75, Economic - 60, B. Std. - 80. Hindi - 55. if weights are 2,3,3,2,1 respectively allotted to the subjects, his weighted mean is

A
$$\displaystyle \frac{50+75+60+80+55}{2+3+3+2+1}$$

B
$$\displaystyle \frac{\left ( 50\times 2 \right )+\left ( 75\times 3 \right )+\left ( 60\times 3 \right )+\left ( 80\times 2 \right )+\left ( 55\times 1 \right )}{5}$$

C
$$\displaystyle \frac{50\times 2+75\times 3+60\times 3+80\times 2+55\times 1}{2+3+3+2+1}$$

D
none

Solution

Percentage marks in the examination-
English=50
Accounts=75
Economics=60
B.Std=80
Hindi=55
Weight allotted to each subjects are-
English=2,Accounts=3,Economics=3,B.std=2 and Hindi=1
Mean=$$\dfrac{sum\ of\ all\ observation\ value}{Sum\ of \ all\ observation}$$
$$\therefore$$ Weight mean=$$\dfrac{50\times 2+75\times 3+60\times 3+80\times 2+55\times 1}{2+3+3+2+1}$$
Question 7
1 / -0

The mean of the following is given by

A
$$10$$

B
$$12$$

C
$$18$$

D
$$20$$

Solution

x f $$f_i.x_i$$
10 3 30
12 10 120
20 15 300
25 7 175
35 5 175
mean$$=\dfrac{\sum f_i.x_i}{\sum f_i}$$
$$\Rightarrow \dfrac{30+120+300+175+175}{3+10+15+7+5}=\dfrac{800}{40}=20$$
Question 8
1 / -0

Which of the following cannot be determined graphically?

A
mean

B
mode

C
median

D
none of these

Solution

$$Mean =\dfrac{Sum of all number}{Total no of numbers}$$
hence mean cannot be determined graphically.
Question 9
1 / -0

If the mean of the following is 15 the value of 'a' is

A
$$4$$

B
$$6$$

C
$$8$$

D
$$10$$

Solution

x f $$f_i.x_i$$
5 6 30
10 a 10a
15 6 90
20 10 200
25 5 125
mean$$=\frac{\sum f_i.x_i}{\sum f_i}$$
$$\Rightarrow15= \dfrac{30+10a+90+200+125}{6+a+6+10+5}$$
$$\Rightarrow 15=\dfrac{445+10a}{27+a}$$
$$\Rightarrow 445+10a=405+a$$
$$\Rightarrow 5a=40$$
$$\Rightarrow a=\dfrac{40}{5}=8$$
Question 10
1 / -0

The median of 1, 3, 6, 8, 4, 2, 7, 10 is

A
6

B
5

C
7

D
5.5

Solution

Arranging in order 1, 2, 3, 4, 6, 7, 8, 10
Median=$$\displaystyle \frac{4+6}{2}=\frac{10}{2}=5$$

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Re-Attempt Weekly Quiz Competition

x	f	fx
3	x	3x
5	x+2	5x+10
6	x-8	6x-48
4	x+6	4x+24

x	f	$$f_i.x_i$$
10	3	30
12	10	120
20	15	300
25	7	175
35	5	175

x	f	$$f_i.x_i$$
5	6	30
10	a	10a
15	6	90
20	10	200
25	5	125

Measures of Central Tendency Test - 15

Result

Measures of Central Tendency Test - 15

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Question 1

$$12$$

$$13$$

$$14$$

$$15$$

Solution

Question 2

$$5$$

$$6$$

$$7$$

$$4$$

Solution

Question 3

$$Rs\ 16$$

$$Rs\ 20$$

$$Rs\ 24$$

$$Rs\ 28$$

Solution

Question 4

5

1

2

3

Solution

Question 5

$$\displaystyle 13^{th}$$

$$\displaystyle 14^{th}$$

$$\displaystyle 15^{th}$$

none of these

Solution

Question 6

$$\displaystyle \frac{50+75+60+80+55}{2+3+3+2+1}$$

$$\displaystyle \frac{\left ( 50\times 2 \right )+\left ( 75\times 3 \right )+\left ( 60\times 3 \right )+\left ( 80\times 2 \right )+\left ( 55\times 1 \right )}{5}$$

$$\displaystyle \frac{50\times 2+75\times 3+60\times 3+80\times 2+55\times 1}{2+3+3+2+1}$$

none

Solution

Question 7

$$10$$

$$12$$

$$18$$

$$20$$

Solution

Question 8

mean

mode

median

none of these

Solution

Question 9

$$4$$

$$6$$

$$8$$

$$10$$

Solution

Question 10

6

5

7

5.5

Solution

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