For which of the following types of variables is it appropriate to calculate an arithmetic mean $x=\frac{\sum x}{n}$?

• A. Ordinal variables
• B. Dichotomous variables
• C. Nominal variables
• D. Interval variables

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the types of variables. Nominal variables represent categories without any order (e.g., colors, names). Ordinal variables have a meaningful order but the intervals between values are not necessarily equal (e.g., rankings). Dichotomous variables have only two categories (e.g., yes/no). Interval variables have ordered categories with equal intervals between values but no true zero point (e.g., temperature in Celsius).
2. Step 2: Recall the definition of the arithmetic mean. The arithmetic mean is the sum of all values divided by the number of values, and it requires numerical data where the differences between values are meaningful and consistent.
3. Step 3: Evaluate each variable type for mean calculation suitability. Nominal variables cannot be averaged because they are categories without numeric meaning. Ordinal variables have order but unequal intervals, so calculating a mean can be misleading. Dichotomous variables are categorical with only two values, so the mean is not typically meaningful.
4. Step 4: Recognize that interval variables have equal intervals between values, making it appropriate to calculate the arithmetic mean since the differences between values are consistent and meaningful.
5. Step 5: Conclude that among the given options, only interval variables are appropriate for calculating the arithmetic mean because they meet the necessary criteria of numeric values with equal intervals.