Final answer:
To calculate the mean of the five distinct numbers, one would sum the numbers and divide by five. The standard deviation involves finding each number's deviation from the mean, squaring these, averaging them, and taking the square root of this average. Specific values are needed for actual calculations.
Step-by-step explanation:
To calculate the mean of the five distinct numbers, you would add all the numbers together and then divide by the number of numbers, which in this case is five. However, since no specific numbers are provided, we cannot calculate an actual mean. The standard deviation is a measure of the amount of variation or dispersion in a set of values.
To calculate it, you subtract the mean from each number to find each number's deviation, square each deviation, find the average of the squared deviations (the variance), and then take the square root of the variance. Again, without specific numbers, we cannot calculate an actual standard deviation.
Examples given in different contexts illustrate how you can calculate the mean and standard deviation in those particular scenarios. Like in the given statistics class example, with a mean of 63 and a standard deviation of 5, or a population example with a mean of 75 and a standard deviation of 4.5.
Remember that in a normally distributed data set, about 68% of values are within 1 standard deviation of the mean, about 95% are within 2 standard deviations, and about 99.7% are within 3 standard deviations.