A key characteristic of the normal distribution is its symmetry. In any symmetric distribution, the mean, median, and mode coincide at the center. Therefore, the median, which is the middle value of the dataset, is exactly equal to the arithmetic mean in a normal distribution.

In a positively skewed distribution, the tail of the distribution extends toward the higher values. This pulls the mean toward the tail, making it larger than the median. Consequently, the median is lesser than the mean in such distributions.

The arithmetic mean is calculated by summing all observations and dividing by the total count. Because it incorporates every value in the dataset, a single extreme outlier can significantly pull the mean toward it, unlike the median or mode, which are more robust to such fluctuations.

The combined mean is calculated using the weighted average formula: (n1*x1 + n2*x2) / (n1 + n2). Here, (650 * 2750 + 700 * 2500) / (650 + 700) = (1,787,500 + 1,750,000) / 1350 = 3,537,500 / 1350, which equals approximately $2,620.37. Rounding to the nearest provided option yields $2,620.

The arithmetic mean is defined as the sum of all values divided by the count. Mathematically, the sum of the differences between each individual observation and the mean is always zero, because the positive deviations exactly cancel out the negative deviations.

The arithmetic mean is calculated by summing all observations and dividing by the count. Here, the sum is 25 and the count is 5, resulting in a mean of 5. Note: The provided answer key (C) is factually incorrect as the mean is 5. This conflict is noted.

A price relative is defined as the ratio of the price of a single commodity in a given period to its price in a base period, multiplied by 100 to express it as a percentage. This is a fundamental component in the construction of simple index numbers.

A simple aggregate price index is calculated by summing the prices of items in the current period and dividing by the sum of prices in the base period. Because it does not account for the quantity or importance of each item, it effectively ignores the relative quantities consumed, which can lead to significant inaccuracies.

In statistics, it is standard practice to use Greek letters to denote population parameters and Roman letters to denote sample statistics. The Greek letter mu (μ) is universally used to represent the population mean, while the Roman letter x-bar (x̅) is used to represent the sample mean. This distinction helps researchers clearly identify whether a value describes an entire population or a subset.

To find the arithmetic mean, sum all the values and divide by the total number of observations. The sum of the 15 values is 11,215. Dividing 11,215 by 15 yields approximately 747.666, which rounds to 747.67. This measure provides the central location of the wage distribution.