How can grouped data hide differences between individual values?

A grouped table replaces individual observations with categories, such as ranges, and reports how many observations belong to each one. That makes the overall pattern easier to scan, but it removes detail: two people’s values can be quite different even when both count in the same range. A frequency table therefore tells you the number of observations in each stated range, not the original observations themselves [S1].

Suppose, as an invented example, five students record how many minutes they read one evening. Their individual times might be 11, 14, 16, 18, and 19 minutes. If the table groups times into 10–19 minutes and shows a frequency of five, you can tell that all five observations fell in that interval. You cannot tell which value belonged to which student—or even whether the values were evenly spread across the interval.

Here is the same invented data shown two ways:

Individual reading times (minutes): 11, 14, 16, 18, 19

Grouped summary: 10–19 minutes: 5 observations

The individual list shows the exact values and their differences. The grouped summary preserves just one fact about them: all five lie within the listed range. Many different lists could produce that same summary—for example, 10, 10, 10, 10, 10 would also give a frequency of five in 10–19. So the table does not establish that the students had similar reading times; it only places their times in the same category.

For a useful comparison, write both versions down and ask, “What detail disappeared when I grouped these values?”

Not exactly from the grouped counts alone. The table does not tell you the individual values, so it does not provide enough information to calculate the exact mean, median, or mode in general. You may be able to estimate a measure of center from grouped frequencies, but an estimate is not the same as recovering the original result [S2].

For instance, if all you know is that five reading times fall between 10 and 19 minutes, their exact mean could vary depending on what those five times were. Do not present a guessed or estimated value as though it came from the original observations. If exact calculations matter, keep or obtain the ungrouped values.

Check the range definitions as well as the counts. The boundaries need clear rules so each value is assigned consistently; otherwise, a value at a boundary might be counted ambiguously [S1]. Also check whether your question needs a broad overview or exact individual detail. Grouping can summarize a distribution, but the table cannot answer questions about a particular observation if it does not list that observation.

For the reading-time example, state exactly which values belong in each interval and label the frequency as a count of observations. If you later need to compare exact values or calculate exact measures of center, retain the original list alongside the grouped summary. The grouped table is a compact view, not a replacement for every detail in the data.