How do missing values change what a table or average represents?
Quick answer
A blank is an unrecorded value, not automatically zero. Count how many entries are present, calculate a summary using only values you can justify including, and say exactly which observations it covers. Missing entries reduce the usable count and may affect how representative the summary is, depending on why values are absent. An average of recorded scores describes those scores—not necessarily everyone in the group. [S1]
The question, the details, the next step.
I have a table with a few empty cells. What should I check before calculating an average?
Check two things: how many values are recorded, and what group a summary of those values describes. A blank means the value is not present in the table; it does not tell you what the value would have been. Missing entries reduce the number of usable observations and can affect how representative a summary is, depending on why the entries are missing. [S1]
Here is an invented example. Assume these are weekly reading minutes reported by five students:
- Student A: 10
- Student B: 20
- Student C: blank
- Student D: 0
- Student E: 30
There are four recorded values, not five. They total 60 minutes, so their mean is 60 ÷ 4 = 15 minutes. Describe this as the average for the four recorded entries. Do not silently count the blank as zero: that would make the calculation 60 ÷ 5 = 12 and treat an unrecorded amount as a measured amount.
Why is the zero different from the blank? They both seem like no reading.
In this example, zero is a recorded value: the table says Student D reported 0 minutes. The blank says no value is recorded for Student C. Those entries could ultimately have the same real-world explanation, but the table alone does not establish that. Keep them distinct unless you have a clear, documented rule for interpreting the blank.
The zero adds nothing to the total but still counts as one recorded observation. The blank contributes neither a known amount nor a usable value. Replacing the blank with zero without evidence makes an assumption that changes what the average represents.
How can I tell whether the average from the recorded values is a fair summary of everyone?
You cannot tell from the arithmetic alone. Ask what the missing entry means and whether there is a reason some values were not recorded. A blank could mean a response was skipped, not collected, or not applicable; these are possibilities to investigate, not conclusions you can draw from the cell itself. Missingness can have different causes and may introduce bias, so consider why values are absent before extending a summary to the full group. [S1]
Report what you know: how many entries were expected, how many were present, and which were included. For the invented table, you could write: “The mean was 15 minutes among the four students with recorded values; one of five entries was blank. This describes the recorded entries, and the table does not show why the value is missing.” That is more precise than saying “the group’s average was 15 minutes.”
Can you give me a reusable way to report this for my own table?
Use this template, filling in only what your table supports:
“Of [number expected] entries, [number present] had recorded values and [number missing] were blank. The [mean/other summary] of the recorded values was [result], calculated using [what was included]. This summarizes [which observations]. The reason for the missing entries is [known reason / not stated], so the result may not represent [broader group] if the missing entries differ from the recorded ones.”
Before sharing the result, check whether a blank is genuinely missing rather than a symbol or category with a separate meaning. If you cannot establish why values are absent, say so instead of guessing. The count and possible causes are worth checking, but a table alone does not establish the reason for a particular blank or quantify its effect on the average. [S1]
A practical checklist
Count entries expected, recorded, and blank.
Keep recorded zeros separate from empty cells.
State which values were included in the calculation.
Label the group the summary actually describes.
Check whether the reason for missing entries is known; do not guess.
If the reason is unknown, say so and avoid claiming the result represents everyone.
A few more useful answers
Should I always leave blank cells out of an average?
Do not treat a blank as a measured number without a justified rule. If you leave it out, report how many recorded values were used and what they represent.
Does a zero count as an observation?
If zero is a recorded measurement, yes: it contributes zero to the total and one to the number of observations. A blank is not a recorded zero.
Can I conclude that missing values caused bias?
Not from a blank cell alone. Missing values can potentially introduce bias, but you need information about why they are missing to assess whether that applies here. [S1]
Sources
References used for this guide.
- [S1] 2.4 Data Cleaning and Preprocessing — Principles of Data Science openstax.org · Checked