Given Information:
- Mean (µ) of the group = 65
- Standard Deviation (SD) of the group = 7.03
- Number of observations in the group = 100

Additional Information:
- Mean (µ) of 60 observations = 70
- Standard Deviation (SD) of 60 observations = 3

To Find:
- Standard Deviation (SD) of the remaining 40 observations

Solution:
Step 1: Calculate the sum of the 100 observations
- Sum = Mean * Number of observations = 65 * 100 = 6500

Step 2: Calculate the sum of the 60 observations with a mean of 70
- Sum_60 = Mean_60 * Number of observations_60 = 70 * 60 = 4200

Step 3: Calculate the sum of the remaining 40 observations
- Sum_40 = Sum - Sum_60 = 6500 - 4200 = 2300

Step 4: Calculate the mean of the remaining 40 observations
- Mean_40 = Sum_40 / Number of observations_40 = 2300 / 40 = 57.5

Step 5: Calculate the sum of the squared differences between each observation and the mean of the remaining 40 observations
- Sum of squared differences (SSD) = Σ(x - Mean_40)^2

Step 6: Calculate the variance of the remaining 40 observations
- Variance = SSD / (Number of observations_40 - 1)

Step 7: Calculate the standard deviation (SD) of the remaining 40 observations
- SD_40 = √Variance

Step 8: Substitute the known values into the equations:
- SSD = Σ(x - Mean_40)^2
- Variance = SSD / (Number of observations_40 - 1)
- SD_40 = √Variance

Step 9: Calculate the sum of the squared differences (SSD)
- SSD = (x1 - Mean_40)^2 + (x2 - Mean_40)^2 + ... + (x40 - Mean_40)^2

Step 10: Calculate the variance
- Variance = SSD / (Number of observations_40 - 1)

Step 11: Calculate the standard deviation (SD)
- SD_40 = √Variance

Step 12: Substitute the values into the equations:
- SSD = (x1 - 57.5)^2 + (x2 - 57.5)^2 + ... + (x40 - 57.5)^2
- Variance = SSD / 39
- SD_40 = √Variance

Therefore, by following these steps, the standard deviation (SD) for the group of 40 observations can be calculated.