Concept: 1 Mark
Application: 3 Marks
Class Interval FrequencyCumulativeFrequency0−105510−20x5+x20−302025+x30−401540+x40−50y40+x+y50−60545+x+yTotal60
n=60
⇒45+x+y=60
⇒x+y=60−45
⇒x+y=15……(1)
The median is 28.5, which lies in the class 20 - 30
So, l = 20, f=20, cf=5+x, h=10
∴ Median=l+(n2−cff)×h
⇒28.5=20+{602−(5+x)20}×10⇒28.5=20+25−x2
⇒25−x2=28.5−20⇒25−x2=8.5
⇒25−x=8.5×2⇒25−x=17
⇒x=25−17=8……(2)
From (1) and (2), 8 + y = 15
⇒y=15−8=7
Hence, the values of x and y are 8 and 7 respectively