Final answer:
The average (arithmetic mean) of a, b, c, and d given a⋅b=3(c⋅d) is (a+b+c+d)/4, which represents the sum of the numbers divided by the number of values.
Step-by-step explanation:
The arithmetic mean of the numbers a, b, c, and d. The equation for the arithmetic mean is the sum of all the values divided by the total number of values. In this case, you add up a, b, c, and d and then divide by 4 to find the mean.
To calculate the sample mean, you would use the values of a, b, c, and d, add them up, and divide by the number of values, which in our case is 4. The sample standard deviation would require a more complex calculation involving each value's deviation from the mean. The comparison between the sample and theoretical measures is significant in statistics, but to answer the given question, we just need to work out the arithmetic mean.
Understanding the distribution for averages is important when dealing with statistics. The Central Limit Theorem suggests that the distribution of sample means tends to be normal, or bell-shaped, as the sample size grows, regardless of the population's distribution. While this information might be more advanced than required for the student's question, it's essential for statistical analysis in general.