Question

mode of the following frequency distribution is 65 and sum of all frequencies is 70

Answer 1

Answer:

x = 14 and y = 2

Step-by-step explanation:

Sum of all the frequencies is given to be 70

⇒ 8 + 11 + x + 12 + y + 9 + 9 + 5 = 70

⇒ 54 + x + y = 70

⇒ x + y = 16 .........(1)

Now, mode is given to be 65

So, our modal class is 60 - 80

$h = 20,l=60,f_1=12,f_2=y,f_0=x\\\\Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h\\\\Mode = 60+\frac{12-x}{2\times 12-x-y}\times 20\\\\65=\frac{1440-60x-60y+320-20x}{24-x-y}\\\\1560-65x-65y=1760-80x-60y\\15x-5y-200=0\\3x-y=40.........(2)$

On adding (1) and (2)

4x = 56

⇒ x = 14

And putting this value of x in equation (1)

14 + y = 16

⇒ y = 2

Answer 2

Answer:

x=10 and y=6

Step-by-step explanation:

from the question we get,

8+11+x+12+y+9+9+5=70,that is x+y=16. --- (equation 1).

now, since mode is 65, which comes under 60-80 range, therefore solution is follows:

mode = l +(f1 -f0) ×h/(2f1 -f0 -f2)

hence, 65=60+ (12-x)/(24 -x-y) ×20

=> 5=12-x/24-(x+y) × 20

=>5= (12-x /24 -16 )×20. ( from eq -1)

=>5= (12-x /2)× 5

=>2=12-x

.•. ,x=10 ,

putting value of x in eq -1,we get

10 +y=16

and hence y=6.

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