Question

given below in the distribution of 140 candidates of obtaining marks x or higher in certain examination calculate the mean marks obtained by candidate's
marks 10 ,20, 30, 40 ,50, 60, 70 ,80, 90, 100
frequency 144, 133, 118, 100, 75, 45, 25, 9, 2, 0​

Answer 1

Answer:

Direct method

size

x

f

xf

0-10

5

20

100

10-20

15

24

360

20-30

25

40

1000

30-40

35

36

1260

40-50

45

20

900

mean =

∑f

∑fx

=

140

3620

=25.857

Assumed mean method

size

x

u=x-25

f

uf

0-10

5

-20

20

-400

10-20

15

-10

24

-240

20-30

25

0

40

0

30-40

35

10

36

360

40-50

45

20

20

400

mean =A+

∑f

∑fu

=25+

140

120

=25.875

Step deviation method

size

x

d=x-25

u=(x-25) / 10

f

uf

0-10

5

-20

-2

20

-40

10-20

15

-10

-1

24

-24

20-30

25

0

0

40

0

30-40

35

10

1

36

36

40-50

45

20

2

20

40

mean =A+h×

∑f

∑fu

=25+10×

140

12

=25.875

Step-by-step explanation:

please mark as brainlist.

Answer 2

Given:

marks 10 ,20, 30, 40 ,50, 60, 70 ,80, 90, 100

frequency 144, 133, 118, 100, 75, 45, 25, 9, 2, 0​

To find:

Mean marks obtained by the candidate.

Solution:

Multiplying each frequency to its corresponding marks and adding all of them to obtain the sum. Dividing this sum obtained by sum of frequency to determine the mean marks of candidate.

Let marks be $x_{i}$ and frequency be $f_{i}$

$x_{i} f_{i}=1440,2660,3540,4000,3750,2700,1750,720,180,0$

Σ$x_{i} f_{i}=1440+2660+3540+4000+3750+2700+1750+720+180+0=20740$

Σ$f_{i}=144+133+118+100+75+45+25+9+2+0=651$

Mean = Σ$x_{i} f_{i}$/Σ$f_{i}$

$Mean=\frac{20740}{651}$

$Mean=31.858$ ≈ $31.86$

Mean marks obtained by the candidate is 31.86