if the mean of the following frequency distribution is 91, find the missing frequency x and y :

classes frequency

0 - 30 12

30-60 21

60 - 90 x

90 -120 52

120 - 150 y

150 - 180 11

total 150

classfrequency (fi)mid-point (xi)xi × fi
0-301215180
30-602145945
60-90x7575x
90-120521055460
120-150y135135y
150-180111651815

Total  150

mean = ∑(xi × fi)/150 = 91

⇒8400+75x+135y = 13650

⇒5x+9y = 350

 

Also, 96+x+y = 150

⇒ x+y = 54

 

solving both equations we get x = 34 and y =20

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