... (3) The following table shows the frequency table of literacy rate (in percentage) of
35 cities. Find the mean literacy rate by assumed mean method :
Literacy rate (in percentage) 45 – 55 55 - 65 65 – 75 75 - 85 85 - 95
Number of cities
310118 3
Take 70 as the assumed mean. Find mean up to two places of decimal.
Answers
Answered by
5
Answer:
We solve this question by assumed mean method.
Mean,
¯¯¯
x
=
a
+
(
∑
f
i
d
i
∑
f
i
)
x¯=a+(∑fidi∑fi)
Steps:
We know that,
Class mark,
x
i
=
Upper class limit
+
Lower class limit
2
xi=Upper class limit + Lower class limit2
Taking assumed mean
,
a
=
70
,a=70
Literacy rate No of cities
(
f
i
)
(fi)
X
i
Xi
d
i
=
x
i
−
a
di=xi−a
f
i
d
i
fidi
45
–
55
45–55
3
3
50
50
−
20
−20
−
60
−60
55
–
65
55–65
10
10
60
60
−
10
−10
−
100
−100
65
–
75
65–75
11
11
70
(
a
)
70(a)
0
0
0
0
75
–
85
75–85
8
8
80
80
10
10
80
80
85
–
95
85–95
3
3
90
90
20
20
60
60
Σ
f
i
=
35
Σfi=35
Σ
f
i
d
i
=
−
20
Σfidi=−20
From the table,we obtain
∑
f
i
=
35
∑
f
i
d
i
=
−
20
∑fi=35∑fidi=−20
Mean
(
¯¯¯
x
)
=
a
+
(
Σ
f
i
d
i
Σ
f
i
)
¯¯¯
x
=
70
+
(
−
20
35
)
¯¯¯
x
=
70
−
4
7
¯¯¯
x
=
70
−
0.57
¯¯¯
x
=
69.43
Mean (x¯)=a+(ΣfidiΣfi)x¯=70+(−2035)x¯=70−47x¯=70−0.57x¯=69.43
Thus, the mean literacy rate is
69.43
69.43%
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