That Can Ruin Your Analysis
— A Field Guide to the Errors Nobody Warns You About —
What your summary statistics are hiding, misrepresenting, and getting dangerously wrong
Here is a belief that quietly ruins more analyses than almost any other: that descriptive statistics are the safe, easy part of data work. You calculate a mean, a standard deviation, maybe a median. You build a table. You label it ‘Summary Statistics’ and move on to the real work the regression, the model, the conclusion.
But descriptive statistics are not a warm-up act. They are the foundation. And foundations built on subtle errors produce conclusions that are confidently, professionally, thoroughly wrong. The frightening part is that none of these mistakes announce themselves. The numbers look fine. The table formats perfectly. The report reads smoothly. The error is invisible until someone with sharper eyes looks at your data, or until reality fails to cooperate with your findings.
This guide walks through the most consequential descriptive statistics mistakes the ones that real analysts, researchers, and students make repeatedly and shows you exactly what goes wrong and how to fix it.
“Descriptive statistics do not speak for themselves. They say whatever your assumptions let them say right or wrong.”
Part 1: Mistakes With Central Tendency
Central tendency mean, median, mode answers the most basic question in data analysis: what is typical? Get this wrong, and every conclusion built on top of it inherits the error.
MISTAKE #1 Using the Mean When Your Data Is Skewed
The arithmetic mean is the workhorse of descriptive statistics. It is also ruthlessly sensitive to extreme values. In a symmetric, bell-shaped distribution, the mean is a perfect summary. But the moment your data develops a long tail as income data, housing prices, hospital stay durations, and response times almost always do the mean stops representing anything typical and starts chasing outliers.
The classic example: if nine people in a room earn $40,000 a year and one person earns $10 million, the mean salary in that room is over $1 million. No single person in the room earns anything close to that. The mean has described a number that nobody actually experiences.
✘ The Mistake: Reporting ‘average income is $1.04M’ when 90% of your sample earns $40,000. Technically correct. Completely misleading.
✔ Better Practice: For skewed distributions, always report the median alongside (or instead of) the mean. The median is resistant to outliers and gives a far more honest picture of what is typical. Include a measure of skewness so your readers can assess the distribution shape themselves.
Rule of Thumb: If your mean and median differ by more than 10-15% of the standard deviation, your distribution is likely skewed enough that the mean alone is misleading.
MISTAKE #2 Ignoring the Mode for Categorical Data
Students learn mean, median, mode as a trio, then spend the rest of their careers ignoring the mode. For numerical data, this is often reasonable. For categorical data, it is a serious analytical failure.
If you’re describing what programming language your team uses most, or what diagnosis appears most frequently in a clinic, or what product category drives most sales the mean and median are meaningless. You cannot average a colour. You cannot find the median of a list of countries. The mode is the only measure of central tendency that applies, and it deserves to be reported clearly and without apology.
✘ The Mistake: Calculating an average of Likert scale responses (1–5) and presenting it as if the mean captures what ‘most people’ felt without checking whether one response category dominated.
✔ Better Practice: For categorical variables, report frequencies and proportions. Report the mode. For ordinal data (like Likert scales), consider reporting the full distribution the proportion in each category rather than collapsing everything to a single number.
MISTAKE #3 Reporting One Measure of Central Tendency and Nothing Else
A single central tendency number, presented alone, is the statistical equivalent of describing a city by its average temperature. Technically informative. Almost completely useless for predicting whether to pack an umbrella.
The mean tells you where the centre is. It tells you nothing about spread, shape, or how representative that centre actually is. Two datasets can have identical means and look nothing alike. One could be tight and symmetric. The other could be wildly bimodal with data clustered at two extremes and nothing near the middle.
Anscombe’s Quartet: In 1973, statistician Francis Anscombe created four datasets with nearly identical means, variances, and correlations — but completely different distributions and shapes. The lesson: summary statistics without visualization can be actively deceptive.
✔ Better Practice: Always pair your central tendency measure with a spread measure (standard deviation, IQR, range), and whenever possible, display a visualization (histogram, box plot, violin plot) so the actual shape of the data is visible.
Part 2: Mistakes With Variability and Spread
If central tendency tells you where your data lives, spread tells you how much of the territory it occupies. Misrepresenting spread is one of the fastest ways to make data look more precise, more stable, or more conclusive than it actually is.
MISTAKE #4 Using Standard Deviation for Non-Normal Data
Standard deviation is a beautiful statistic for normally distributed data. It tells you that roughly 68% of observations fall within one standard deviation of the mean, 95% within two. These properties are powerful and intuitive. They also depend entirely on the data being roughly normal.
Apply standard deviation to heavily skewed data and those percentages become fiction. Worse, standard deviation can suggest that negative values are plausible reporting ‘mean response time: 200ms, SD: 300ms’ mathematically implies some responses happened before the stimulus. Nobody flags this. Everyone reads the table and moves on.
✘ The Mistake: Reporting mean ± SD for income data, healthcare costs, or any metric with a hard floor of zero and a long upper tail. The implied range will include impossible values.
✔ Better Practice: For skewed data, use the Interquartile Range (IQR) the range from the 25th to the 75th percentile — as your spread measure. It is robust to outliers and always describes a plausible range of typical values. Report as median [IQR: Q1 – Q3].
MISTAKE #5 Confusing Standard Deviation With Standard Error
This is arguably the most common quantitative mistake in published research, including peer-reviewed papers. Standard deviation (SD) and standard error (SE) are not interchangeable. They answer different questions. Using the wrong one — especially to make your results look more precise is a form of misrepresentation, even if unintentional.
Standard Deviation describes the spread of individual data points around the mean. It tells you about variability in your sample. It does not shrink as sample size grows (beyond stabilizing around the true population SD).
Standard Error describes the precision of your estimate of the mean. It equals SD divided by the square root of n. It gets smaller as your sample grows not because the data is less variable, but because your estimate of the mean is more precise.
The trap: SE is always smaller than SD. Researchers who want their data to look more consistent sometimes report SE in contexts where SD is appropriate making results appear tighter and more reliable than they are.
✘ The Mistake: Plotting error bars as ±SE when the question is ‘how variable are individual measurements?’ Using SE gives bars half the size of SD bars, creating a false impression of data tightness.
✔ Better Practice: Use SD when describing the spread of your data. Use SE (or confidence intervals) when describing the precision of a statistical estimate. Always label your error bars explicitly ‘error bars = SD’ or ‘error bars = 95% CI’ — and never leave readers to guess.
MISTAKE #6 Presenting Range Without Context
The range maximum minus minimum is the most seductive and most misleading spread statistic in existence. It is easy to calculate, easy to understand, and almost entirely determined by the two most extreme values in your dataset. One unusual data point can double your range overnight.
Reporting ‘salaries ranged from $28,000 to $4.2 million’ might be technically accurate while being practically useless. That $4.2 million could be one founder’s compensation in a company of 200 people. The range implies a kind of continuity across that span that may not exist at all.
✔ Better Practice: Supplement the range with the IQR or a percentile summary (e.g., 5th to 95th percentile) to give a more honest picture of where the bulk of your data sits. Consider also reporting how many data points lie in the extreme tails.
Part 3: Mistakes With Distributions and Shape
Two datasets can have identical means and standard deviations and be completely, fundamentally different. Shape matters. Ignoring it is how subtle disasters hide in plain sight.
MISTAKE #7 Never Visualizing Your Data — Trusting Only the Numbers
There is a version of data analysis that happens entirely in tables. Numbers go in. Summary statistics come out. Conclusions are drawn. No one ever looks at what the data actually looks like.
This is dangerous. Summary statistics can mask bimodal distributions (two humps in your data suggesting two distinct subgroups). They can hide floor and ceiling effects (data piling up at the maximum or minimum of your scale). They can obscure the presence of outliers that are not extreme enough to break your statistics but extreme enough to distort them.
Always Remember: The four datasets in Anscombe’s Quartet all have: mean of X = 9, mean of Y = 7.5, variance of X = 11, variance of Y = 4.12, correlation = 0.816, and the same regression line. Plot them and they look completely, shockingly different.
✘ The Mistake: Running descriptive statistics on a new dataset without first producing a histogram or density plot for each continuous variable and a frequency bar chart for each categorical variable.
✔ Better Practice: Make data visualization the first step, not an afterthought. For every continuous variable, produce a histogram. For every categorical variable, produce a frequency table and bar chart. Look for multimodality, skewness, outliers, and unexpected gaps before calculating a single summary statistic.
MISTAKE #8 Treating Outliers as Errors and Silently Removing Them
Outliers make analysts uncomfortable. They stretch scales, skew distributions, and complicate the clean story you were trying to tell. So they get removed. Sometimes with a note in the methods section. Sometimes without.
But outliers are not automatically errors. They are data points. Sometimes they represent measurement error a typo, a sensor malfunction, a data entry mistake. In that case, correction or removal is justified. But sometimes outliers represent the most interesting cases in your dataset the patient who responded dramatically to treatment, the customer who spent ten times the average, the city that broke every economic trend.
Removing outliers to tidy up your statistics, without investigating what they represent, is a form of analytical dishonesty even when it is done innocently.
✘ The Mistake: Removing all values more than 2 SD from the mean as ‘outliers’ without checking whether those values are genuine data points, and without reporting that removal was done.
✔ Better Practice: Investigate every outlier before touching it. Is it a data entry error? Document and correct. Is it a legitimate extreme value? Report the analysis with and without it. Never silently delete. Always report your outlier handling policy in your methods.
MISTAKE #9 Ignoring Bimodal or Multimodal Distributions
A bimodal distribution one with two distinct peaks is your data’s way of telling you something important: there may be two different populations mixed together in your sample. Reporting a single mean for bimodal data is like reporting the average temperature of a room where one half is 10°C and the other half is 40°C. The ‘average’ of 25°C describes neither half accurately.
This happens constantly in practice. You survey employees about job satisfaction and get a bimodal distribution some employees are very satisfied, others very dissatisfied, with few in the middle. The mean comes out moderate. The conclusion: ’employees have moderate satisfaction.’ The reality: you have a deeply divided workforce and a potential retention crisis.
✘ The Mistake: Reporting mean satisfaction as 3.1/5 without noticing (or reporting) that responses cluster at 1-2 and 4-5 with almost nobody in the middle.
✔ Better Practice: Always check for multimodality by visualizing distributions. If you find multiple modes, investigate whether they represent distinct subgroups. Segment your analysis accordingly report descriptive statistics for each subgroup separately rather than forcing a single summary onto a mixed population.
Part 4: Mistakes With Percentages and Proportions
Percentages feel simple. They are not. They are among the most frequently misused numbers in data communication, in ways that can reverse the apparent meaning of your findings entirely.
MISTAKE #10 Percentage Change vs. Percentage Point Change
This distinction trips up journalists, executives, policymakers, and researchers with alarming regularity and the difference can change the entire meaning of a reported number.
Percentage Point Change: The arithmetic difference between two percentages. If unemployment goes from 4% to 6%, that is a 2-percentage point increase.
Percentage Change: The relative change calculated as (new – old) / old × 100. That same shift from 4% to 6% is a 50% increase in the unemployment rate.
Both are technically correct. Both describe the same data. They produce radically different impressions. A politician who wants to dramatize a problem will report the 50% increase. One who wants to minimize it will report the 2-percentage point rise. Neither is lying. Both may be misleading their audience.
✘ The Mistake: Writing ‘our conversion rate improved 100%’ when it went from 1% to 2% — technically a 100% relative increase, practically a 1 percentage point gain that may be within the margin of noise.
✔ Better Practice: Always specify which type of change you are reporting. Whenever both numbers are meaningful, report both. Make the base rate explicit so readers can assess the magnitude for themselves.
MISTAKE #11 Ignoring Base Rates — The Small Denominator Problem
‘Sales in our new region grew 200% last quarter!’ Impressive. Unless last quarter’s sales in that region were three units. A jump from 3 to 9 units is technically 200% growth and practically irrelevant.
Small denominators make percentages explode. One extra case in a rare disease cohort of 10 people is a 10% increase in incidence. The same additional case in a population study of 10,000 is 0.01%. The underlying event one person getting sick is identical. The percentage is wildly different. Reporting only the percentage, without the base count, hides this entirely.
✘ The Mistake: Reporting percentage growth, percentage improvement, or percentage risk without stating the absolute numbers from which those percentages were calculated.
✔ Better Practice: Always report absolute numbers alongside percentages. ‘200% growth (from 3 to 9 units)’ is honest. ‘200% growth’ alone invites misinterpretation. In health and risk research, report both absolute risk and relative risk.
Part 5: Mistakes With Presentation and Reporting
Even correctly calculated statistics can be communicated in ways that mislead. The final stage how you present your descriptive statistics carries as much responsibility as the calculations themselves.
MISTAKE #12 False Precision — Reporting Too Many Decimal Places
There is something deeply convincing about a number like 47.3821%. It looks measured. Rigorous. Scientific. The question is whether it actually is. Reporting four decimal places on a survey of 80 people implies a precision your sample size cannot support. It is statistical theater the appearance of exactness without the substance.
The appropriate number of decimal places depends on your sample size, your measurement instrument’s precision, and what level of detail is actually meaningful for decision-making. Reporting the mean age of your sample as 34.7 years is usually sufficient. Reporting it as 34.7143 years adds nothing and implies a precision that does not exist.
✘ The Mistake: Reporting ‘mean score = 72.4829 out of 100’ for a 5-item Likert survey with 45 respondents. The instrument and sample cannot support that precision.
✔ Better Practice: Match your decimal places to your measurement precision and sample size. For most social and behavioral research, one or two decimal places are sufficient. Round thoughtfully not to make numbers look cleaner, but to accurately reflect what your data can tell you.
MISTAKE #13 Summary Tables With No Units, No Context, No Sample Size
A table of summary statistics that does not report the unit of measurement, the sample size for each statistic, and the time period or population it describes is a table that cannot be evaluated, replicated, or trusted. Yet these omissions appear in professional reports, academic papers, and business dashboards with startling regularity.
What is a mean of 47.3? Is that seconds, dollars, patients, kilograms? Is it based on 15 observations or 15,000? Is it from last year’s data or aggregated over a decade? Without these anchors, the number floats free of any interpretive ground.
✘ The Mistake: Publishing a table with rows labeled ‘Mean,’ ‘SD,’ ‘Min,’ ‘Max’ and no column headers specifying variables, no row noting sample size, and no caption explaining what the data represents or when it was collected.
✔ Better Practice: Every summary statistics table should include: the variable name and unit of measurement, the sample size (n) for each statistic, the time period and population covered, and a caption that explains what the table shows and any important caveats.
Quick Reference: Mistakes, Signals, and Fixes
Use this table as a checklist when reviewing your own descriptive statistics before reporting them.
| Mistake | Warning Signal | The Fix |
| Mean on skewed data | Mean and median differ substantially | Report median + IQR instead |
| SD on non-normal data | Data has outliers or hard zero floor | Use IQR; report median |
| SD vs SE confusion | Error bars look suspiciously small | Label error bars clearly; use SD for spread |
| No visualization | Only a table of numbers in your report | Add histograms and box plots first |
| Silent outlier removal | Suspicious round sample sizes | Document all exclusions in methods |
| Bimodal data averaged | Mean is ‘moderate’ but few values are near it | Segment analysis by subgroup |
| % change without base | Large % change from small absolute number | Report absolute numbers alongside % |
| False precision | 4+ decimal places on small sample | Round to 1-2 decimal places |
| Incomplete tables | No units, no n, no time period | Add full context to every table |
The Bigger Picture: Why This Matters Beyond Statistics
Descriptive statistics are usually the first thing a reader, a client, or a policymaker sees. They set the frame. They establish the baseline. They shape every interpretation that follows. When they are wrong even subtly, even unintentionally the entire analysis is compromised, because every conclusion is built on a foundation that doesn’t hold.
The mistakes in this guide are not obscure edge cases. They are common, recurring, and consequential. They appear in peer-reviewed journals, government reports, corporate dashboards, and news articles. They influence hiring decisions, medical protocols, product launches, and public policy.
The solution is not a more sophisticated statistical technique. It is discipline and honesty at the most basic level: look at your data before you summarize it, choose your statistics to match your data’s actual properties, and present your results with enough context that a careful reader could evaluate them independently.
That discipline not the algorithm, not the software is what separates analysis that informs from analysis that merely persuades.
“The purpose of descriptive statistics is to describe reality accurately. When we choose them to confirm what we want to find, we stop doing analysis and start doing advocacy.”