The number of observations in a survey is 40. If the mean of the first 10 observations is 4.5 and that of remaining is 3.5, then the mean of the whole survey is
- A2.82
- B3.80
- C3.75
- D4.25
Solution & Step-by-step Explanation
Let's use the properties of weighted averages to find the total combined mean:
Total observations (N): 40
First group (n
1
): 10 observations with mean (
x
ˉ
1
) = 4.5
Sum of first group=n
1
×
x
ˉ
1
=10×4.5=45
Second remaining group (n
2
): 40−10=30 observations with mean (
x
ˉ
2
) = 3.5
Sum of second group=n
2
×
x
ˉ
2
=30×3.5=105
Total mean (
X
ˉ
):
Total Sum=45+105=150
X
ˉ
=
Total Observations
Total Sum
=
40
150
=
4
15
=3.75
Total observations (N): 40
First group (n
1
): 10 observations with mean (
x
ˉ
1
) = 4.5
Sum of first group=n
1
×
x
ˉ
1
=10×4.5=45
Second remaining group (n
2
): 40−10=30 observations with mean (
x
ˉ
2
) = 3.5
Sum of second group=n
2
×
x
ˉ
2
=30×3.5=105
Total mean (
X
ˉ
):
Total Sum=45+105=150
X
ˉ
=
Total Observations
Total Sum
=
40
150
=
4
15
=3.75