Best examples of comparing means with descriptive statistics examples in 2025

Real-world examples of comparing means with descriptive statistics examples

Let’s start where people actually live: concrete situations. Below are several examples of comparing means with descriptive statistics that show up in day‑to‑day analysis long before anyone opens a stats textbook.

Think of each as a mini case study: we’re not running formal hypothesis tests yet. We’re just using descriptive statistics to compare means, look at spread, and decide whether a difference is interesting enough to investigate further.

Health example of comparing means: blood pressure before vs. after treatment

Imagine a clinic testing a new lifestyle program for adults with high blood pressure. They measure systolic blood pressure (SBP) for 60 patients before and after three months in the program.

Descriptive summary:

• Before program: mean SBP = 148 mmHg, standard deviation = 12
• After program: mean SBP = 136 mmHg, standard deviation = 11

This is one of the clearest examples of comparing means with descriptive statistics examples:

• The mean dropped from 148 to 136, a 12‑point reduction.
• The standard deviations are similar, so the spread of values didn’t change much.

Without any formal test, you can already say:

• On average, participants ended the program with lower blood pressure.
• The change is large enough (12 mmHg) to be clinically meaningful according to guidelines from sources like the NIH and CDC.

You’d still run a paired t‑test later, but descriptive statistics give you a first, intuitive picture. This kind of example of comparing means is common in medical quality improvement projects.

Education example of comparing means: test scores across classrooms

A school district wants to see whether a new math curriculum is associated with higher test scores. Two seventh‑grade classrooms use the new curriculum; two others use the old one. At the end of the year, the district summarizes the scores.

New curriculum (2 classes, 52 students):

• Mean score = 82
• Standard deviation = 9

Old curriculum (2 classes, 49 students):

• Mean score = 77
• Standard deviation = 14

This is a textbook education example of comparing means with descriptive statistics:

• The new curriculum group has a higher mean (82 vs. 77).
• The old curriculum group has much higher variability (SD 14 vs. 9).

Why does this matter?

• The higher mean suggests the new curriculum may be associated with better performance.
• The larger spread in the old curriculum suggests outcomes are more inconsistent, with some students doing very well and others struggling.

Before any formal inference, these descriptive statistics help the district decide whether it’s even worth investing in a larger, more rigorous study.

For context, national discussions about math performance and curriculum design show up regularly in reports from organizations like the National Center for Education Statistics, which often publish tables of means and standard deviations by state, gender, or program type. Those tables are themselves real examples of comparing means with descriptive statistics.

Business example of comparing means: sales by region

Consider a retail company evaluating quarterly sales performance across three regions: West, Midwest, and South. Each region has dozens of stores, and analysts summarize average quarterly revenue per store.

West (n = 40 stores):

• Mean quarterly revenue = $420,000
• Standard deviation = $60,000

Midwest (n = 35 stores):

• Mean = $380,000
• Standard deviation = $45,000

South (n = 38 stores):

• Mean = $395,000
• Standard deviation = $90,000

This is one of the best examples of comparing means with descriptive statistics examples in a business context:

• The West leads on average revenue.
• The South shows higher variability (SD $90,000), suggesting some stores are booming while others lag.

From descriptive statistics alone, management might:

• Investigate outliers in the South (both top performers and underperformers).
• Ask whether the higher mean in the West is due to demographics, pricing, or marketing.

Again, no regression yet. Just comparing means and spreads to prioritize where to dig deeper.

Sports example of comparing means: player performance across seasons

Sports analytics lives on examples of comparing means with descriptive statistics. Take a basketball player whose points per game (PPG) are tracked across three recent seasons.

Season A (2021–22):

• Mean PPG = 18.4
• Standard deviation = 5.2

Season B (2022–23):

• Mean PPG = 20.1
• Standard deviation = 4.8

Season C (2023–24):

• Mean PPG = 19.7
• Standard deviation = 6.1

By simply comparing means:

• There’s an uptick from Season A to B, then a slight dip in Season C.
• Variability increases in Season C, suggesting more inconsistency.

Coaches and analysts might combine this descriptive comparison with context:

• Did the player’s role change?
• Were there injuries?
• Did team pace or offensive strategy shift?

Sites that track advanced stats often start with descriptive tables of means and standard deviations. Those tables are real examples of how analysts compare performance over time.

Public health example of comparing means: BMI by age group

Public health agencies constantly compare means across demographic groups. Suppose a health department summarizes body mass index (BMI) from a 2024 community survey.

Age 18–34 (n = 500):

• Mean BMI = 26.2
• Standard deviation = 4.1

Age 35–54 (n = 620):

• Mean BMI = 28.7
• Standard deviation = 4.6

Age 55+ (n = 450):

• Mean BMI = 29.1
• Standard deviation = 4.9

This is another straightforward example of comparing means with descriptive statistics:

• Mean BMI increases with age group.
• The spread (standard deviation) is similar but slightly larger in older groups.

Public health teams might compare these descriptive results with national data from the CDC’s National Health and Nutrition Examination Survey. If local means are higher than national means, that flags a potential problem and justifies targeted interventions.

Again, the first step is just comparing descriptive means and spreads across age groups, not jumping immediately into regression models.

Education and equity example: comparing means by demographic groups

In 2025, there’s growing attention on equity metrics in schools and universities. A university might compare average first‑year GPA across demographic groups to monitor equity.

Suppose they summarize GPAs for a 2024 entering cohort:

• Group A: mean GPA = 3.12, SD = 0.45
• Group B: mean GPA = 2.95, SD = 0.51
• Group C: mean GPA = 3.08, SD = 0.49

This is a sensitive but important example of comparing means with descriptive statistics examples:

• Differences in means are modest but noticeable.
• Standard deviations are similar, so spread is comparable.

The university should not jump to conclusions about causes based only on descriptive comparisons. But these examples of comparing means help identify where to ask better questions:

• Are there differences in high school preparation?
• Are support resources distributed fairly?

Research from institutions like Harvard’s Graduate School of Education often starts with descriptive comparisons of means by demographic group before moving to more complex models.

Time-series example: comparing means before and after a policy change

Policy analysts often work with “before vs. after” examples of comparing means with descriptive statistics. Imagine a city that lowered speed limits on residential streets in mid‑2023. Analysts compare average monthly traffic accidents per 10,000 residents.

Before policy (Jan 2022–Jun 2023, 18 months):

• Mean accidents = 5.4 per 10,000
• Standard deviation = 1.1

After policy (Jul 2023–Dec 2024, 18 months):

• Mean accidents = 4.1 per 10,000
• Standard deviation = 0.9

Descriptive comparison shows:

• A reduction of 1.3 accidents per 10,000 residents on average.
• Slightly lower variability after the policy.

This example of comparing means doesn’t prove causation by itself (other factors may have changed), but it’s a strong starting signal that the policy might be working. Many public reports from transportation departments feature exactly this kind of descriptive before‑and‑after mean comparison.

How to interpret examples of comparing means with descriptive statistics examples

Now that we’ve walked through several examples of comparing means with descriptive statistics, it’s worth stepping back to see what they have in common and how to interpret them responsibly.

Across all these cases:

• You’re comparing a central tendency (often the mean) across groups, time periods, or conditions.
• You’re pairing the mean with at least one measure of spread (usually standard deviation, sometimes range or interquartile range).
• You’re using sample size as context: a 5‑point difference in means from 10 people is very different from the same difference from 10,000 people.

When you see examples of comparing means with descriptive statistics examples, ask yourself:

• Is the difference in means large enough to matter in the real world? In blood pressure, a 2‑point shift is small; a 12‑point shift is meaningful.
• Is variability similar across groups? Huge differences in standard deviation can change how you interpret the means.
• Are sample sizes similar? A mean from 30 people is less stable than a mean from 3,000.
• Could there be confounding factors? For example, comparing BMI across age groups without considering activity level, income, or health status.

Descriptive comparisons of means are an early warning system. They tell you where to look harder and which questions deserve more advanced modeling.

Connecting descriptive comparisons to inferential statistics

A lot of students and analysts treat descriptive and inferential statistics as two separate worlds. In reality, the best examples of comparing means with descriptive statistics examples are the ones that naturally lead to the right inferential tools.

From the examples above:

• The blood pressure before/after case points toward a paired t‑test or repeated measures analysis.
• The classroom curriculum comparison suggests an independent samples t‑test or ANOVA if more groups are added.
• The sales by region case hints at ANOVA across three or more regions.
• The policy change example points toward interrupted time‑series analysis or difference‑in‑differences if there’s a comparison city.

But you don’t start there. You start with descriptive means, standard deviations, maybe a quick visualization, and only then decide which inferential method is appropriate.

If you look at statistical guidance from universities (for example, introductory resources from UCLA’s statistics pages), they almost always begin with descriptive comparisons of means before introducing hypothesis tests.

FAQ: common questions about examples of comparing means with descriptive statistics

Q1. Can you give a simple example of comparing means with descriptive statistics for beginners?
A very simple example of comparing means is comparing average study time between two groups of students. Suppose Group 1 studies an average of 6 hours per week (SD = 2), and Group 2 studies 4 hours per week (SD = 1.5). Just from these descriptive statistics, you can say Group 1 studies more on average and has slightly more variation in study time.

Q2. How many groups can I compare with descriptive means?
There’s no hard limit. Descriptive statistics can summarize means for any number of groups. The challenge is interpretability: once you have more than four or five groups, it becomes harder to keep track of all the comparisons. That’s where tables and visualizations help. But you can still create examples of comparing means with descriptive statistics examples across many categories, like age bands, regions, or product lines.

Q3. Are differences in means always meaningful if they’re statistically significant later?
No. With very large datasets, tiny differences in means can be statistically significant but practically irrelevant. Descriptive comparisons help you sense whether a difference matters in the real world before you run tests. For instance, a 0.1‑point difference in GPA might be statistically significant in a sample of 50,000 students but not meaningful for advising policy.

Q4. Should I always use the mean when comparing groups?
Not always. If your data are skewed or have extreme outliers (like income or hospital length of stay), the median can be more informative. However, many examples of comparing means with descriptive statistics in practice still use the mean because it connects directly to many inferential methods and is easy to interpret if the distribution isn’t too skewed.

Q5. Where can I find real examples of comparing means with descriptive statistics in official data?
Look at summary tables from organizations like the CDC, NIH, or NCES. Their reports often include tables showing average values (means) and standard deviations by gender, age, region, or year. Those tables are real, high‑stakes examples of comparing means with descriptive statistics examples used to guide policy and funding decisions.

Comparing means with descriptive statistics is not just a classroom exercise. It’s how hospitals evaluate treatments, schools judge programs, businesses spot growth opportunities, and governments monitor public health. If you can read and create these examples of comparing means with descriptive statistics, you’re already doing meaningful statistical analysis—even before you open a single formula sheet.