Question

The mode of the following frequency distribution of 165 observations is 38:

find value of a and b.​

Answer 1

Answer:

Step-by-step explanation:

mode = $l+(\frac{f_1-f_0}{2f_-f_0 -f_2})h$

let,

l = 32

f₀ = a

f₁ = 53

f₂ = b

$38 = 32+(\frac{53-a}{2*53-a-b} )9$

$6 = (\frac{53-a}{106-a-b} )9$

$\frac{6}{9} =(\frac{53-a}{106-a-b} )$

$6(106-a-b)=9(53-a)$

$636-6a-6b=477-9a$

$159=-3a-6b$

$53 = -a-2b$  (taking out 3 common) -----------eq.1.

Now, 8+13+a+53+b+18+12 = 165

94+a+b = 165

a+b = 71 ------eq.2.

now, eq.1.+eq.2.

-a-2b+a+b=53+71

-b = 124

b = -124

53 = -a - 2(-124)

53 = -a + 248

a = 195

hope it helps...