Question

Find mean, median and mode
more than - 150 140. 130. 120. 110. 100. 90. 80
Frequency - 0. 12. 27. 60. 105. 124. 141 150

Answer 1

Byselectingclassesforthegivendataas:80−90,90−100,100−110,110−120,120−130,130−140,140−150Wewritethefrequencydistributionasbelow:

Class interval (C.I)	Frequency (f)	Cumulative Frequency (c f)
80 - 90	150 - 141 = 9	9
90 - 100	141 - 124 = 17	26
100 - 110	124 - 105 = 19	45
110 - 120	105 - 60 = 45	90
120 - 130	60 - 27 = 33	123
130 - 140	27 - 12 = 15	138
140 - 150	12 - 0 = 12	150

Hence,n= 150 ⇒n2=75Now,110−120istheclasswhosecumulativefrequency90isgreaterthan75.Hence,medianclassis110−120.Thus,l=110,n2=75,cf=45,f=45andh=10Therefore,Median=l+{( n/2−cf)/f}×h=110+{75−4545}×10=110+{3045}×10=110+23×10=110+203=110+6.67=116.67