The frequencies of Observation 4, 7, 8 ,10, 11 are respectively 3f-4, f + 1 , 2f+ 1 ,f+2, f -1. If the mean of frequency distribution is 8, find the frequency of observation 8 and also find the total frequency
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Answer:
⇒ Here, modal class =32−41
⇒ l=32,f
0
=a,f
1
=53,f
2
=b and h=9
⇒ Mode=l+
2f
1
−f
0
−f
2
f
1
−f
0
×h
⇒ 34.5=32+
2×53−a−b
53−a
×9
⇒
9
2.5
=
106−a−b
53−a
⇒ 265−2.5a−2.5b=477−9a
⇒ 7.5a−2.5b=212
⇒ 75a−25b=2120
∴ 13a−5b=424 ------ ( 1 )
As total observation are 165
⇒ So, 5+11+a+53+b+16+10=165
⇒ 95+a+b=165
∴ a+b=70 -------- ( 2 )
∴ b=70−a
Substitute b=70−a in equation ( 1 )
⇒ 13a−5(70−a)=424
⇒ 13a−350+5a=424
⇒ 18a=424+350
⇒ 18a=774
∴ a=43
⇒ b=70−43=27
∴ Frequency a=43 and b=27
Explanation:
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