The mode of the following data is 154. Find the . . .

Question : The mode of the following data is 154. Find the value of m. Also find median of following data.

Class Intervals	120-130	130-140	140-150	150-160	160-170
Frequency	2	8	m	20	8

Doubt by Parth 

Solution : 

Mode = 154
Modal Class = 150-160
l=150
h=160-150=10
f₀=m
f₁=20
f₂=8

Mode = l+{[f₁-f₀]/[2f₁-f₀-f₂]}×h
154 = 150+{[20-m]/[2(20)-m-8]}×10
154-150= {[20-m]/[40-m-8]}×10
4/10 = {[20-m]/[32-m]}
2/5 = [20-m]/[32-m]
2[32-m] =5[20-m]
64-2m=100-5m
5m-2m=100-64
3m=36
m=36/3
m=12

Median of the Data 

Class Intervals (CI)	Frequency (fi)	Cumulative Frequency (CF)
120-130	2	2
130-140	8	10
140-150	12	22
150-160	20	42
160-170	8	50
	N=Σfi=50

Here 

N=Σf_i=50
N/2 = 50/2 = 25

Median class = 150-160

l=150

h=160-150=10
CF=22
f=20

Median = l+{[(N/2)-CF]/[f]}×h
Median = 150+{[25-22]/[20]}×10
Median = 150+30/20
Medina = 150+3/2

Median = 150+1.5
Median = 151.5