There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is −3.5. The mean of the given numbers is
- A49.5
- B53.5
- C46.5
- D56.5
Solution & Step-by-step Explanation
Let the original numbers be x
1
,x
2
,…,x
50
and their true mean be
x
ˉ
.
According to the question, each element x
i
is subtracted from 53. The new transformed data values are (53−x
i
).
By linear properties of the arithmetic mean:
Mean(53−x)=53−Mean(x)
We are given that the mean of the new data points is −3.5:
53−
x
ˉ
=−3.5
53+3.5=
x
ˉ
x
ˉ
=56.5
Thus, the mean of the original group of numbers is 56.5.
1
,x
2
,…,x
50
and their true mean be
x
ˉ
.
According to the question, each element x
i
is subtracted from 53. The new transformed data values are (53−x
i
).
By linear properties of the arithmetic mean:
Mean(53−x)=53−Mean(x)
We are given that the mean of the new data points is −3.5:
53−
x
ˉ
=−3.5
53+3.5=
x
ˉ
x
ˉ
=56.5
Thus, the mean of the original group of numbers is 56.5.