The mean number of hours spent per day on the computer, according to a national survey, is six hours, with a standard deviation of 2.5 hours. If each time was increased by 1.5 hours, what would be the new mean and standard deviation?

In the given case, each value of the original data is increased by 1.5, so the mean for the new data set will also be increased by 1.5. Therefore, the new means will be = 6 + 1.5 = 7.5 hours

However, standard deviation stays the same i.e. 2.5 hours. Standard deviation stays the same because the difference between the mean and the data value stays the same because both of them are being increased by the same quantity. As a result, the sum of squared deviations stay the same as was in original case and hence the value of standard deviation stays the same.

Lets assume that original values in data are a, b and c with a mean of 6. When each of them are increased by 1.5, the new values would be a + 1.5, b + 1.5 and c + 1.5. So, now the mean would be:

[tex]\frac{a+1.5+b+1.5+c+1.5}{3}\\\\ =\frac{a+b+c+4.5}{3}\\\\ =\frac{a+b+c}{3}+\frac{4.5}{3} \\\\ =\frac{a+b+c}{3}+1.5\\\\ =6+1.5\\\\ =7.5[/tex]

This example illustrates that if each value of the data is increased by a same number, the mean would also be increased by the same number.

So, new mean would be 7.5 hours and standard deviation would be 2.5 hours.