find mean median and mode of the following frequency distribution plzz....
Answers
Step-by-step explanation:
Class (f) (cf) M. P fm
0-10 |4| 4 5 20
10-20 |6| 10 15 90
20-30 |8| 18 25 200
30-40 |12| 30 35 420
40-50 |10| 40 45 450
50-60 |5| 45 55 275
60-70 |5| 50 65 325
sum=50 sum=1760
n=50/2=25
Mean=1760/50=35.2
The c. f just greater than 25 is 30 and corresponding class is 30-40,so modal class is 30-40.
Now, l=30,h=10,f=12,c.f=c.f of preceding class=18
Median= l+{h × n/2-cf/f}
=30+{10×25-18/12}
=30+{10×7/12}
=30+{5×7/6}
=30+{35/6}
=180+35/6
=215/6
=35.83
Mode=3(median)-2(mean)
=3×35.83-2×35.2
=107.49-70.4
=37.09
OR
Mode=l+(f1-f0/2 f1-f0-f2) ×h
=30+(12-8/2×12-8-10) ×10
=30+(4/6) ×10
=30+20/3
=90+20/3
=36.66 or 37