Final answer:
Adding a constant to every score in a distribution increases the mean by that constant but does not change the standard deviation.
Step-by-step explanation:
When a constant is added to every score in a distribution, the mean of the distribution will increase by that constant, but the standard deviation will remain unchanged. The standard deviation is a measure of variability or spread in a set of data. It indicates how much the individual data points differ from the mean. If we simply add a constant to each data point, all points shift by the same amount, and therefore, their relative positions and the overall variability remain the same.
To illustrate with an example, consider a set of data points {2, 4, 6}. The mean is 4, and the standard deviation is approximately 1.63. If we add a constant, say 3, to each data point, our new set is {5, 7, 9}. The new mean is 7, but the standard deviation remains approximately 1.63, because the shape of the distribution hasn't changed; it has only shifted.