The mean of the following data is 42, find the missing frequencies x and y if the sum of the - Maths -

Question

The mean of the following data is 42, find the missing frequencies
x and y if the sum of the frequencies is 100

Class interval

0−10

10−20

20−30

30−40

40−50

50−60

60−70

70−80

Frequency

7

10

x

13

y

10

14

9

Global Expert · Accepted Answer

The given data is shown as follows:

Class interval

Frequency
(fi)

Class mark (xi)

fixi

0−10

7

5

35

10−20

10

15

150

20−30

x

25

25x

30−40

13

35

455

40−50

y

45

45y

50−60

10

55

550

60−70

14

65

910

70−80

9

75

675

Total

∑ fi = 63 + x + y

∑ fixi = 2775 + 25x +
45y

Sum of the frequencies = 100

⇒∑ifi=100⇒63+x+y=100⇒x+y=100-63⇒x+y=37⇒y=37-x    
(1)

Now, The mean of given data is given by

x¯=∑ifixi∑ifi⇒42=2775+25x+45y100⇒4200=2775+25x+45y⇒4200-2775=25x+45y⇒1425=25x+45(37-x)      from (1)⇒1425=25x+1665-45x⇒20x=1665-1425⇒20x=240⇒x=12

If x = 12, then y = 37 − 12 = 25

â€‹Thus, the value of x is 12 and
y is 25

Class interval	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency	7	10	x	13	y	10	14	9

Class interval	Frequency *(f_i)*	*Class mark (x_i)*	*f_ix_i*
0−10	7	5	35
10−20	10	15	150
20−30	x	25	25x
30−40	13	35	455
40−50	y	45	45y
50−60	10	55	550
60−70	14	65	910
70−80	9	75	675
Total	∑ f_i = 63 + x + y		∑ f_ix_i = 2775 + 25x + 45y

The mean of the following data is 42, find the missing frequencies x and y if the sum of the frequencies is 100. Class interval 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80 Frequency 7 10 x 13 y 10 14 9

The mean of the following data is 42, find the missing frequencies x and y if the sum of the frequencies is 100.

Class interval 0−10 10−20 20−30 30−40 40−50 50−60 60−70 70−80

Frequency 7 10 x 13 y 10 14 9