5. The mean of the following frequency distribution is 576 and the sum of the observations is 50
Find f, and f
Class 0-20 20 40 40-60 60 80 80-100 100-120
Frequency
7
f1
12
f2
8
5
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Answer:
Class Frequency
(
f
i
)
(fi) Mid values
(
x
i
)
(xi)
(
f
i
×
x
i
)
(fi×xi)
0-20 7 10 70
20-40
f
1
f1 30 30
f
1
f1
40-60 12 50 600
60-80 18-
f
1
f1 70 1260-70
f
1
f1
80-100 8 90 720
100-120 5 110 550
Total
∑
f
i
=
50
∑fi=50
∑
(
f
i
×
x
i
)
=
3200
−
40
f
1
∑(fi×xi)=3200-40f1
We have:
7
+
f
1
+
12
+
f
2
+
8
+
5
=
50
7+f1+12+f2+8+5=50
⇒
f
1
+
f
2
=
18
⇒f1+f2=18
⇒
f
2
=
18
–
f
1
⇒f2=18–f1
∴ Mean, x =
Σ
i
(
f
i
×
x
i
)
Σ
i
f
i
Σi(fi×xi)Σifi
⇒ 57.6 =
3200
−
40
f
1
50
3200−40f150
⇒
40
f
1
=
320
⇒40f1=320
∴
f
1
=
8
∴f1=8
A
n
d
f
2
=
18
–
8
And f2=18–8
⇒
f
2
=
10
⇒f2=10
∴ The missing frequencies are
f
1
=
8
and
f
2
=
10
.
f1=8andf2=10.
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