Standard deviation
The mean of a distribution of scores is the average.
Variance
Variance
You can't do this without knowing the distribution of scores.
They are said to be Normally distributed.
The distribution is skewed to the right.
If most the population has many high scores, the distribution is negatively skewed. If most have many low scores, it is positively skewed
z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
This simply means that if you plot a histogram of the scores it will be asymmetric.
If the distribution is Gaussian (or Normal) use z-scores. If it is Student's t, then use t-scores.
The IQs of a large enough population can be modeled with a Normal Distribution
The advantage of a grouped frequency distribution is that it is small enough for you to get a pretty good idea at a glance how the scores are distributed. The disadvantage is that you are lumping scores together, thus losing some of the information in the original scores.