Question

from the following data find out D2,D7 and D9​

Answer 1

Solution :-

Marks -------- Fi --------- CF

0 - 10 --------- 4 ----------- 4

10 - 20 -------- 9 -----------13

20 - 30 --------14 ----------27

30 - 40 --------25 ---------52

40 - 50 --------18 ----------70

50 - 60 -------- 6 ----------76

60 - 70 ---------2 ----------78

70 - 80 ---------1 -----------79

80 - 90 ---------1 -----------80

90 - 100 --------0 ----------80

now, we know that,

• Di = l + (N*i/10 - cf) * (h/f)

so, we get,

• N = Total frequency = 80
• h = class interval = 10

now, for D2 :-

• class = (2N/10) = (2*80/10) = 16 = CF greater than 16 is 27 corresponding to 20 - 30 .
• l = lower limit = 20
• i = 2
• cf = cumulative frequency of the class preceding the class = 13
• f = frequency of D2 = 14

then,

→ D2 = 20 + [80*2/10 - 13] * (10/14)

→ D2 = 20 + (16 - 13) * (5/7)

→ D2 = 20 + (15/7)

→ D2 = 22.14

now, for D7 :-

• class = (7N/10) = (7*80/10) = 56 = CF greater than 56 is 70 corresponding to 40 - 50 .
• l = lower limit = 40
• i = 7
• cf = cumulative frequency of the class preceding the class = 52
• f = frequency of D7 = 18

then,

→ D2 = 40 + [80*7/10 - 52] * (10/18)

→ D2 = 40 + (56 - 52) * (5/9)

→ D2 = 40 + (20/9)

→ D2 = 42.22

now, for D9 :-

• class = (9N/10) = (9*80/10) = 72 = CF greater than 72 is 76 corresponding to 50 - 60 .
• l = lower limit = 50
• i = 9
• cf = cumulative frequency of the class preceding the class = 70
• f = frequency of D9 = 6

then,

→ D2 = 50 + [80*9/10 - 70] * (10/6)

→ D2 = 50 + (72 - 70) * (5/3)

→ D2 = 50 + (10/3)

→ D2 = 53.33

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Answer 2

Given:

Refer to an attachment

To find:

$D_{2}, D_{7}, D_{8}$

Solution:

Marks.                 freq.              cumulative freq.

0-10                       4                           4

10-20                     9                          13      

20-30                    14                         27

30-40                    25                        52

40-50                    18                         70

50-60                     6                          76

60-70                      2                          78

70-80                      1                           79

80-90                      1                           80

90-100                     0                          80

N=80

Finding D2:

2n/10 = 2(80)/10 =16

So, decile class is 20-30

L=20, F=14, CF=13, H=10

$D_{2} = L +\dfrac{(\dfrac{2n}{10} - cf)}{f} \times h$

$=> D_{2} = 20 +\dfrac{16 - 13}{14} \times 10$

$=> 20+2.14$

$=> 22.14$

Finding D7:

7n/2 = 7(80)/10 =56

So, decile class is 40-50

L=40, F=18, CF= 52, H=10

$D_{7} = L +\dfrac{(\dfrac{7n}{10} - cf)}{f} \times h$

$=> D_{7} = 40 +\dfrac{56 - 52}{18} \times 10$

$=> 40+2.22$

$=>42.22$

Finding D9:

9n/2 = 9(80)/10 = 72

So, decile class is 50-60

L=50, F=6, CF= 70, H=10

$D_{9} = L +\dfrac{(\dfrac{9n}{10} - cf)}{f} \times h$

$=> D_{9} = 50 +\dfrac{72 - 70}{6} \times 10$

$=> 50 + 3.33$

$=> 53.33$