9.5 Comparing Two or More Data Sets

Comparison Is the Actual Exam Task

The NLN content outline for Data and Information lists three expected outcomes. One is computing the mean, median, and mode(s) of a data set — the work of Section 9.3. The other two are problem-solving outcomes: use summary statistics of real-value data to compare two or more data sets, and interpret data plots or tabular information to identify meaning, patterns, relationships, or trends.

That distinction matters for how you study. Data and Information is 17.5% of the test (7 scored items), and the NLN blueprint splits it 3 computation / 4 problem solving. So the majority of the items in this area are not "find the mean of these five numbers" — they are "here are two groups; which one is higher, steadier, or improving faster?" Computing a statistic is the setup. Comparing is the question.

The Comparison Workflow

1. Compute the same statistic for every set. Never compare a mean to a median.
2. Pair a center with a spread. Mean or median tells you where the data sits; range tells you how scattered it is. One without the other is an incomplete comparison.
3. Check whether the group sizes match. If they do not, compare rates or means, not totals.
4. Re-read which statistic the question named. "Higher average," "more consistent," and "larger increase" are three different questions with three different answers.

Same Center, Different Spread

This is the single most tested comparison idea, because it is the one that looks counterintuitive.

Ward A: sum = 68 + 72 + 76 + 80 + 84 = 380, so mean = 380 ÷ 5 = 76 bpm. Ordered, the middle value is 76 bpm, so the median is 76. Range = 84 − 68 = 16 bpm.

Ward B: sum = 60 + 66 + 76 + 86 + 92 = 380, so mean = 76 bpm. Median = 76 bpm. Range = 92 − 60 = 32 bpm.

The two wards have the same mean and the same median. If the question asks which ward has the higher average, the honest answer is neither. But Ward B's range is twice as wide, so Ward B's patients are far less consistent. A question asking which ward is "more stable" or "more consistent" is asking about spread, and the answer is Ward A.

When the Mean and the Median Disagree

An outlier in one set can flip the ranking depending on which statistic you use.

Clinic A wait times (min): 10, 12, 14, 15, 99. Clinic B wait times (min): 20, 22, 24, 26, 28.

By the mean, Clinic B is faster. By the median, Clinic A is much faster — four of its five patients waited 15 minutes or less, and a single 99-minute wait dragged the mean up by 16 minutes. Both readings are mathematically correct; they answer different questions. The exam expects you to notice the outlier and to use whichever statistic the item names.

The general rule from Section 9.3 still holds: the mean is sensitive to outliers and the median is robust. In a comparison, that sensitivity is exactly what can reverse your answer.

Unequal Group Sizes: Compare Rates, Not Counts

When two groups are different sizes, raw totals are meaningless. Convert to a rate — a count divided by the size of the group it came from.

Ward A: 8 falls over 200 patient-days → 8 ÷ 200 = 0.04 = 4 falls per 100 patient-days. Ward B: 12 falls over 400 patient-days → 12 ÷ 400 = 0.03 = 3 falls per 100 patient-days.

Ward B recorded more falls but has the lower rate. Ward A is the unit with the safety problem. Any comparison that stops at "12 is bigger than 8" gets this backwards, and this exact shape — bigger raw number, smaller rate — is a standard NEX distractor.

The same logic applies to test scores across differently sized classes, medication errors across units, and infection counts across months of different lengths. Ask yourself: count out of how many?

Absolute Change vs Percent Change

Comparing trends adds one more distinction, carried over from Section 9.4.

Site B grew by twice as many units. Site A grew faster in relative terms. "Which site increased the most?" is ambiguous; "which site had the largest percent increase?" is not. Read the wording before you compute.

Which Statistic Answers Which Question

Common Traps

1. Comparing unlike statistics. Set A's mean against Set B's median is not a comparison. Compute the same measure for both.
2. Ignoring spread. Two sets with identical means can behave completely differently. Report a center and a spread together.
3. Comparing raw counts across unequal groups. Always ask "out of how many?" and convert to a rate.
4. Assuming the bigger absolute change is the bigger percent change. The base matters; a small base makes a small change look large.
5. Not re-reading the question. "Higher," "more consistent," and "faster growing" point at three different statistics in the same data set.