According to these data, the mean time students spent on the exam was 94.1 minutes, and the standard deviation was 24.23 minutes. Suppose the exam proctor realized after compiling these data that he had used the wrong start time in his calculation, so that each value for time spent on exam needs to be reduced by 15 minutes. He also wants to express the times in hours, rather than minutes. Find the mean and standard deviation of the transformed data.

Well, it looks like the proctor really needs to work on his time management skills! But don't worry, I'm here to help.

To find the mean of the transformed data, we simply need to subtract 15 minutes from the original mean and then convert it to hours.

Mean of transformed data = (Mean of original data - 15) / 60

Mean of transformed data = (94.1 - 15) / 60 = 79.1 / 60 = 1.32 hours

Next, let's find the standard deviation of the transformed data. Since we are only subtracting a constant value from each data point, the standard deviation does not change.

So, the standard deviation of the transformed data remains the same at 24.23 minutes.

But since the proctor wants the times expressed in hours, we need to convert the standard deviation to hours as well.

Standard deviation of transformed data = 24.23 / 60 = 0.4048 hours (approximately)

So, the mean of the transformed data is 1.32 hours and the standard deviation is approximately 0.4048 hours.

Now, let's hope the proctor checks his start time properly next time!

To find the mean and standard deviation of the transformed data, you need to apply the given changes to the original data.

1. Start by reducing each value in the dataset by 15 minutes. This will shift the data by 15 minutes to the left.

2. Next, convert the times from minutes to hours. Divide each value by 60, since there are 60 minutes in an hour.

Let's calculate the mean and standard deviation of the transformed data step-by-step:

Step 1: Calculate the new mean
To find the new mean, subtract 15 from the original mean and then divide by 60 to convert it from minutes to hours.
New Mean = (94.1 - 15) / 60 = 79.1 / 60 ≈ 1.318 hours

Step 2: Calculate the new standard deviation
To find the new standard deviation, divide the original standard deviation by 60 to convert it from minutes to hours.
New Standard Deviation = 24.23 / 60 ≈ 0.404 hours

So, the mean of the transformed data is approximately 1.318 hours, and the standard deviation is approximately 0.404 hours.

To find the mean and standard deviation of the transformed data, we need to apply two transformations to the original data: subtracting 15 minutes and converting minutes to hours.

1. Subtracting 15 minutes from each value:
To do this, we subtract 15 from each individual value in the original data.

2. Converting minutes to hours:
To convert minutes to hours, we divide each value (which has already been reduced by 15 minutes) by 60.

After applying these transformations, we can calculate the mean and standard deviation of the transformed data.

Let's go step by step:

1. Subtracting 15 minutes from each value:
Subtract 15 minutes from each value of the original data set. For example, if a student spent 100 minutes on the exam, after subtracting 15, we would have 100 - 15 = 85 minutes.

2. Converting minutes to hours:
After subtracting 15 minutes from each value, divide each value by 60 to convert minutes to hours. For example, if a student spent 85 minutes on the exam (after subtracting 15), we would have 85 / 60 = 1.4167 hours.

3. Calculate the mean of the transformed data:
To find the mean of the transformed data, sum up all the values and divide by the total number of values. Add up all the values obtained after applying the transformations (subtracting 15 and converting to hours), and then divide by the total number of values.

4. Calculate the standard deviation of the transformed data:
To find the standard deviation of the transformed data, we need to calculate the variance first. The variance is the average of the squared differences from the mean. Then take the square root of the variance to obtain the standard deviation.

After performing these calculations, you will have the mean and standard deviation of the transformed data.

Mean = (94.1-15)/60

Since every score is reduced by the same amount, the SD remains the same.

SD = 24.23/60