You are given the following:

there are 27 pieces of data
mean is 60
standard deviation is 25

You realize that one of the pieces of data is inputted wrong..... it was a 25, but it is suppose to be 52.... find the actual mean and standard deviation for the actual set of numbers

It was supposed to be 52 instead of 25, so that adds 27 to the total to calculate the mean. The mean rises by 1 to 61. The standard decreases since the correct value is closer to the mean. It appears it should decrease by 1 to 24, but I'll let you prove that.

To calculate the new mean for the actual set of numbers, we need to adjust for the incorrect data point by subtracting the incorrect value (25) and adding the correct value (52) to the original sum of the data. Since there are 27 pieces of data, we can calculate the new sum by subtracting 25 from the original sum and adding 52.

Original sum = mean * number of data = 60 * 27 = 1620
New sum = Original sum - incorrect value + correct value
= 1620 - 25 + 52
= 1647

Now, we can calculate the new mean by dividing the new sum by the total number of data points, which is still 27.

New mean = New sum / number of data = 1647 / 27 ≈ 61.00

Therefore, the actual mean for the new set of numbers is approximately 61.00.

To calculate the new standard deviation, we need to adjust for the incorrect data point's effect on the deviation from the mean. Since the correct value (52) is closer to the new mean (61) than the incorrect value (25), the standard deviation should decrease.

You can prove this by recalculating the standard deviation for the original set of data and then comparing it to the calculated standard deviation for the new set of data. To calculate the standard deviation, we need to know the individual data points.

Once you have the individual data points, you can use the following formula to calculate the standard deviation:

Standard deviation = √(Σ(xi - mean)² / n)

Where:
- Σ(xi - mean)² represents the sum of the squared deviations of each data point from the mean
- n is the number of data points

By substituting the actual mean (61) and the correct data values into the formula, you can calculate the standard deviation for the new set of data.