Question

Calculate the mode for the following frequency distribution.

Class	Frequency
0-10	5
10-20	8
20-30	7
30-40	12
40-50	28
50-60	20
60-70	10
70-80	10

mode is 4.67
If true then enter $1$ and if false then enter $0$

Answer 1

Range(Xi)	Freq(Fi)	Cum Freq
0 to 10	5	5
10 to 20	8	13
20 to 30	7	20
30 to 40	12	32
40 to 50	28	60	Modal range
50 to 60	20	80
60 to 70	10	90
70 to 80	10	100
Total	100

$Mode=l+\frac{(f_m-f_{m-1})}{(f_m-f_{m-1})+(f_m-f_{m+1})}\times wlisthelowerclassboundaryofthemodalclassinterval;f_{m-1}isthefrequencyofthegroupbeforethemodalclassinterval.f_{m}isthefrequencyofthemodalclassinterval;f_{m+1}isthefrequencyofthegroupafterthemodalclassinterval.wisthewidthoftheclassinterval.Heremodalrangeis40-50.l=40,f_m=28,f_{m-1}=12,f_{m+1}=20,w=10Mode=40+\frac{28-12}{(28-12)+(28-20)}\times 10=40+\frac{16\times 10}{16+8}=40+\frac{160}{24}=40+\frac{20}{3}=40+6.67=46.67$