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Standard deviation is a measure that describes how much individual scores or data points deviate from the mean, or average, of a dataset. In simpler terms, it tells us how spread out the scores are. The larger the standard deviation, the more spread out the numbers are. For example, if a golfer has a mean score of 85 with a small standard deviation, it means most of their games have scores close to 85. If the standard deviation is large, the scores are more varied (sometimes much higher or lower than 85).
To compute the standard deviation of the total 18 hole score from the original exercise, we start by finding the variance for each 9-hole game, and since the games are independent, we add these variances together. The total variance is 242, so the standard deviation—being the square root of variance—is approximately 15.56. This indicates a moderate spread in his total golf scores over 18 holes.

Variance is another statistical measure that helps us understand data dispersion. It is the average of the squared differences from the Mean. It is particularly useful because it is part of the process to calculate standard deviation.
In our golfer example, the variance for each 9-hole segment is found by squaring the standard deviation 11, resulting in 121. Since each 9-hole game score is independent, we sum these variances to find the total variance over 18 holes, which turns out to be 242. By understanding variance, we can see that it gives us the "spread squared" and helps in reaching the standard deviation.

Independent variables in statistics are those whose occurrence is not influenced by other variables. When dealing with golf scores or any sequential activities, it's essential to establish such independence to calculate aggregate variances correctly.
In the exercise, the scores from the first and second 9-hole rounds are treated as independent. This means the outcome of one does not affect the other. Because of this, the variance of the total score is simply the sum of the individual variances from each half of the game. Without independence, we'd need additional methods to compute the total score's statistics.

The normal distribution, often referred to as the bell curve, is a common way to model data that clusters around a mean. It assumes that data near the mean are more frequent in occurrence than data far from the mean. This supports much of statistical analysis due to its properties of symmetry and predictable variability.
In this exercise, the assumption of a normal distribution is useful because it suggests the golfer's scores are evenly spread around the mean (85 per 9 holes). Given a normal distribution, we can confidently apply the rules for calculating mean and standard deviation for combined data. The second 9-hole round having the same distribution properties allows for tidy computations and explanations of the golfer's full 18-hole performance.