Which statement is true about grouped data?

Which statement is true about grouped data?

• A. The sum of X can always be determined from class marks.
• B. Real limits are the exact class endpoints.
• C. The total of frequencies equals the sample size.
• D. The median cannot be estimated from grouped data.

Answer: (C)

In grouped data, each observation fits into one class interval, and you add up the frequencies across all intervals. Since every observation is counted exactly once, the sum of all class frequencies equals the total number of observations in the dataset—that is, the sample size. This is why that statement is true. The other ideas rely on approximations or definitions that don’t hold exactly. The sum of X isn’t determined exactly from class marks alone because class marks are midpoints used for estimation, not the actual values. Real limits aren’t simply the stated endpoints; they are the true boundaries that define what data could fall into a class, often offset by a half-unit in continuous data. And the median can be estimated from grouped data by locating the median class and interpolating within it, so it’s not correct to say it cannot be estimated.

In grouped data, each observation fits into one class interval, and you add up the frequencies across all intervals. Since every observation is counted exactly once, the sum of all class frequencies equals the total number of observations in the dataset—that is, the sample size. This is why that statement is true.

The other ideas rely on approximations or definitions that don’t hold exactly. The sum of X isn’t determined exactly from class marks alone because class marks are midpoints used for estimation, not the actual values. Real limits aren’t simply the stated endpoints; they are the true boundaries that define what data could fall into a class, often offset by a half-unit in continuous data. And the median can be estimated from grouped data by locating the median class and interpolating within it, so it’s not correct to say it cannot be estimated.