Question

The grades, out of 60, for a math test have a mean of 25 and a standard deviation of 4. To get a percentage mark, Mrs. Adams doubles all the scores and adds 4 points.

Write down the new mean and new standard deviation.

Answer 1

The new mean is 54 and the new standard deviation is 8.

Step-by-step explanation:

To find the new mean and new standard deviation after doubling the scores and adding 4 points, we need to use the properties of means and standard deviations.

First, let's find the new mean. Since each score is doubled and 4 points are added, the new mean will be:

New Mean = (2 x Mean) + 4

Substituting the given mean value of 25:

New Mean = (2 x 25) + 4 = 54

Next, let's find the new standard deviation. When each score is doubled, the standard deviation also doubles. So the new standard deviation will be:

New Standard Deviation = 2 x Standard Deviation

Substituting the given standard deviation value of 4:

New Standard Deviation = 2 x 4 = 8