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Standard deviation is a statistical measurement that offers a glimpse into the amount of variation or dispersion present in a set of values. In simpler terms, it tells you how spread out the numbers are in a dataset.
For example, if the scores of a class on a test are tightly clustered around the mean (average) score, the standard deviation will be low, implying that most students scored similarly.
Conversely, a high standard deviation indicates that the scores are spread over a wider range, showing significant differences from the mean score. To calculate the standard deviation, one would summarize how much each score in the data set varies from the mean and then it is typically averaged out. This calculation provides insight into the consistency of the scores.
In the context of the given exercise, the standard deviation is 20, which means if we were to pick any score at random, there鈥檚 a reasonable chance it would fall within 20 points above or below the mean.

The term 'mean score' refers to the average of a set of numbers, and it is calculated by adding up all the values in a dataset and dividing by the number of values.
For a normally distributed set of scores, the mean represents the center point of the distribution, with half of the scores lying above this point and half lying below. It is a crucial measure because it allows us to assess an individual score within the context of the overall group performance.
For instance, a mean score of 100 in our exercise indicates that, on average, students scored 100 on the test. Any individual score can be compared against this average to determine whether it is above or below the typical performance.

The concept of 鈥榥ormally distributed scores鈥� pertains to a probability distribution that is symmetrical about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
In a normal distribution, scores are spread in a specific way that follows a bell-shaped curve when graphed. The '68-95-99.7 rule' illustrates this distribution, indicating that approximately 68% of the values fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
This characteristic pattern means that in our exercise, most test scores will hover around the mean of 100 with decreasing frequency as you move away from it. Consequently, a score that is two standard deviations above the mean, which calculates to 140, is relatively high and is better than the vast majority of the scores.