Fill in the table and solve the following questions Using Dm

Fill in the table and solve the following questions (Using D-method).

Given

Fx method

d-method

Class Interval

f

X

X²

cf

fX

fX²

d

fd

d²

fd²

30-34

3

-2

35-39

7

-1

40-44

11

0

45-49

22

1

50-54

40

2

Total

Mean

Median

Mode

Range

Variance

Standard deviation

Quartile 1^st

Fill in the table and solve the following questions (Using D-method).

Given

Fx method

d-method

Class Interval

f

X

X²

cf

fX

fX²

d

fd

d²

fd²

2 - 12

5

7

-1

12 - 22

7

17

0

22 - 32

5

27

1

32 - 42

3

37

2

Total

Mean

Median

Mode

Range

Variance

Standard deviation

Quartile 1^st

Given	Fx method	d-method
Class Interval	f	X	X2	cf	fX	fX2	d	fd	d2	fd2
30-34	3						-2
35-39	7						-1
40-44	11						0
45-49	22						1
50-54	40						2
Total

Solution

Mean = sum(fX)/sumf = 3931/83 = 47.36

Median = L + ((n/2-F)/f)*i

L = lower boundary of class median

i = class width

n = sum of frequency

F = cumlative frequency before class medium

f = frequency of class median

n/2 = 41.5 which is 3rd median class i.e. 40-44

f = 11 F = 10 i=5 L = 39.5

median = 39.5 + (41.5-10)/11 * 5 = 39.5+14.3 = 53.8

1st quartile = L_Q1 + ((n/4-F)/f_Q1)*i

L = lower boundary of class 1st quartile

i = class width

n = sum of frequency

F = cumlative frequency before class 1st quartile

f = frequency of class 1st quartile

n/4 = 41.5 which is 3rd median class i.e. 40-44

f = 11 F = 10 i=5 L = 39.5

median = 20.75 + (20.75-3)/7 * 5 = 20.75+12.67 = 33.42

mode = 39.5 + 18/(40+18)*5 = 39.5 + 1.55 = 41.05

Variance = (sum of fX^2 - (sum of fX)^2/n)/(n-1) = (188817 - 3931^2/83)/82 = 32.185

Std. deviation = sqrt(variance) = 5.67

range = 54-30 = 24

Class Interval	f	X	X^2	Cf	fX	fX^2	d	fd	d^2	fd^2
30-34	3	32	1024	3	96	3072	-2	-6	4	12
35-39	7	37	1369	10	259	9583	-1	-7	1	7
40-44	11	42	1764	21	462	19404	0	0	0	0
45-49	22	47	2209	43	1034	48598	1	22	1	22
50-54	40	52	2704	83	2080	108160	2	80	4	160
Sum	83	210	9070		3931	188817		89	10	201