The mean age of a herd is 7.9 years. a cow that is 0.5 years old is added to the herd . how does this cows age affect the mean

By definition, mean is the summation of data values divided by number of data values. In the current scenario, a mean of a data is given. When the number of the herd is added by one while the data value added is less than the mean, then the new mean is expected to reduce. The opposite would happen, that is: the new mean would increase if the data value added was greater than the mean.

In the current case, therefore, the new mean age of the herd will be less than 7.9 years.