A data set of n observations has mean 2x, While another data set of 2n observations has mean x. Then the mean of the combined data set of 3n observations will be:
Answers
Mean is the sum of the data values divided by the total number of values.
Given that, mean of n observations is 2
x
ˉ
⟹2
x
ˉ
=
n
sum of n observations
Therefore, sum of n observations is 2
x
ˉ
n ------(1)
Given that, mean of 2n observations is
x
ˉ
⟹
x
ˉ
=
2n
sum of 2n observations
Therefore, sum of 2n observations is 2
x
ˉ
n ------(2)
Mean of the combined data set is
n+2n
sum of n observations + sum of 2n observations
⟹mean=
n+2n
2
x
ˉ
n+2
x
ˉ
n
(from (1) and (2))
⟹mean=
3n
4
x
ˉ
n
⟹mean=
3
4
x
ˉ
Answer:
Step-by-step explanation:
If a data set of n observation has mean 2x, then the total for the n observations is
If a data set of 2n observations has mean x, then the total for the 2n observations is
The sum total for the 2 data sets (n+2n) is;
The mean for the combination of the two data sets is
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