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Byju's Answer
Standard IX
Mathematics
Mean
If X -is the ...
Question
If
X
¯
is the mean of x
1
,x
2
,.......,x
n
, then for
a
≠
0
, the mean of ax
1
,ax
2
,......,ax
n
,
x
1
a
,
x
2
a
,
.
.
.
,
x
n
n
is
(
a
)
a
+
1
a
X
¯
(
b
)
1
2
a
+
1
a
X
¯
(
c
)
a
+
1
n
X
¯
n
(
d
)
a
+
1
a
X
¯
2
n
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Solution
It is given that, the mean of x
1
, x
2
,..., x
n
is
X
¯
.
∴
X
¯
=
x
1
+
x
2
+
.
.
.
+
x
n
n
Mean
=
Sum
of
observations
Number
of
observations
⇒
x
1
+
x
2
+
.
.
.
+
x
n
=
n
X
¯
.....(1)
Now,
a
x
1
,
a
x
2
,
.
.
.
,
a
x
n
,
x
1
a
,
x
2
a
,
.
.
.
,
x
n
a
are 2n observations.
∴ Mean of these observations
=
a
x
1
+
a
x
2
+
.
.
.
+
a
x
n
+
x
1
a
+
x
2
a
+
.
.
.
+
x
n
a
2
n
=
a
x
1
+
x
2
+
.
.
.
+
x
n
+
1
a
x
1
+
x
2
+
.
.
.
+
x
n
2
n
=
a
+
1
a
x
1
+
x
2
+
.
.
.
+
x
n
2
n
=
a
+
1
a
×
n
X
2
n
[Using (1)]
=
1
2
a
+
1
a
X
Thus, the mean of
a
x
1
,
a
x
2
,
.
.
.
,
a
x
n
,
x
1
a
,
x
2
a
,
.
.
.
,
x
n
a
is
1
2
a
+
1
a
X
.
Hence, the correct answer is option (b).
Suggest Corrections
0
Similar questions
Q.
If
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then for
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(b)
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(d)
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Q.
If
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is the mean of
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,
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, then for
a
≠
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, the mean of
a
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,
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Q.
Question 16
If
¯
x
is the mean of
x
1
,
x
2
,
…
…
x
n
,
then for
a
≠
0
,
the mean of
a
x
1
,
a
x
2
,
…
…
a
x
n
,
x
1
a
,
x
2
a
,
…
…
x
n
a
is:
A)
(
a
+
1
a
)
¯
x
B)
(
a
+
1
a
)
¯
x
2
C)
(
a
+
1
a
)
¯
x
n
D)
(
a
+
1
a
)
¯
x
2
n
Q.
Which is false?
(a) If
x
is the mean of
x
1
,
x
2
,
.
.
.
,
x
n
, then
∑
i
=
1
n
(
x
i
-
x
)
=
0
.
(b) If the mean of
x
1
,
x
2
,
.
.
.
,
x
n
is
x
, then the mean of
(
x
1
+
a
)
,
(
x
2
+
a
)
,
.
.
.
,
(
x
n
+
a
)
i
s
(
x
+
a
)
.
(c) If the mean of
x
1
,
x
2
,
.
.
.
,
x
n
is
x
and
a
≠
0
, then the mean of
a
x
1
,
a
x
2
,
.
.
.
,
a
x
n
is
a
x
.
(d) If M is the median of
x
1
,
x
2
,
.
.
.
,
x
n
and
a
≠
0
, then aM is the median of
a
x
1
,
a
x
2
,
.
.
.
a
x
n
.
Q.
Question 16
If
¯
x
is the mean of
x
1
,
x
2
,
…
…
x
n
,
then for
a
≠
0
,
the mean of
a
x
1
,
a
x
2
,
…
…
a
x
n
,
x
1
a
,
x
2
a
,
…
…
x
n
a
is:
A)
(
a
+
1
a
)
¯
x
B)
(
a
+
1
a
)
¯
x
2
C)
(
a
+
1
a
)
¯
x
n
D)
(
a
+
1
a
)
¯
x
2
n
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