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Byju's Answer
Standard VII
Mathematics
Arithmetic Mean and Range
The mean weig...
Question
The mean weight of 8 numbers is 15 kg. If each number is multiplied by 2, what will be the new mean?
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Solution
Let x
1
, x
2
, x
3
...x
8
be the eight numbers whose mean is 15 kg. Then,
15
=
x
1
+
x
2
+
x
3
+
...
+
x
8
8
x
1
+
x
2
+
x
3
+
.
.
.
+
x
8
=
15
×
8
⇒
x
1
+
x
2
+
x
3
+
.
.
.
+
x
8
=
120.
Let the new numbers be 2x
1
, 2x
2
, 2x
3
, ...2x
8.
Let M be the arithmetic mean of the new numbers.
Then,
ā
M
=
2
x
1
+
2
x
2
+
2
x
3
+
....
+
2
x
8
8
=
>
M
=
2
(
x
1
+
x
2
+
x
3
+
....
x
8
)
8
=
>
M
=
2
×
120
8
=
>
M
=
30
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The mean of
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numbers is
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the new mean will be:
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Mean of 12 numbers is 20 if each number is multiplied by 3 what will be the new mean?
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