We know that,
Mean of the distribution (¯x)=∑5i=1fixi∑5i=1fi=50 [given]
⇒f1x1+f2x2+f3x3+f4x4+f5x5f1+f2+f3+f4+f5=50
⇒(17)(10)+(5a+3)(30)+(32)(50)+(7a−11)(70)+(19)(90)17+5a+3+32+7a−11+19=50
⇒170+150a+90+1600+490a−770+171012a+60=50
⇒3570−770+640a12a+60=50
⇒2800+640a=600a+3000
⇒40a=200⇒a=5
∴ Frequency of 30 =5a+3=5(5)+3 [put a=5]
=25+3=28
And frequency of 70=7a−11=7(5)−11 [put a=5]
=35−11=24
Hence, the frequencies of 30 and 70 are 28 and 24 respectively.