DNP 830 Topic 5: quantitative methods of inquiry
Three measures of centre on the same variable, and where they disagree is the finding. A submission that reports all three and comments on none has done the arithmetic and skipped the inquiry.
Editorial process
Last reviewed · August 15, 2026
Means, medians and modes on data that has a shape
This exercise asks for three measures of centre, and the reason it asks for three rather than one is that their relationship carries information. In a symmetric distribution the mean, median and mode sit close together. When the mean pulls above the median, the distribution has a long right tail — a few large values dragging the average, which in clinical data usually means a handful of very long stays, very high costs or very high readings. When the mode sits well away from both, the distribution may be bimodal, which frequently signals two populations quietly combined in one dataset. Reporting the three numbers is the easy part. Saying what their arrangement implies about the data is the assignment. None of this survives being read off the output alone, which is why the exercise asks for interpretation: the same three numbers describe a tidy symmetric variable and a badly contaminated one, and only their relationship tells you which you have.
That leads directly to the practical judgement the exercise is training. Which centre should you report as the summary? For a skewed variable the median describes the typical case better, while the mean remains the right quantity if you care about a total — total bed days across a unit depend on the mean, not the median, however skewed the distribution is. So the answer depends on the claim being made, and saying which claim you have in mind is more sophisticated than a rule about skewness. Be careful with the mode in SPSS: on a continuous variable it is often meaningless, and where several values tie, the software reports the smallest and adds a footnote almost everyone misses. Check the footnote, and say in your write-up when a mode should not be interpreted at all. The same caution applies to a median over very few cases, where one more patient moves it noticeably.
Likely learning objectives
Inferred from the brief — check these against your own rubric.
- 01Interpret the relationship between mean, median and mode as evidence about distribution shape.
- 02Choose a measure of centre according to the claim being made.
- 03Recognise bimodality as a sign of combined populations.
- 04Know when a mode should not be interpreted.
Read the full question
Review every instruction before using the planning guidance that follows.
Course-wide instructions that accompany this question
Name: Assignment Rubric DNP 830 Topic 5 Quantitative Methods of Inquiry Grid View List View Excellent Good Fair Poor Summarize your interpretation of the frequency data provided in the output for respondent’s age, highest school grade completed, and family income from prior month. 32 (32%) – 35 (35%) The response accurately and clearly explains, in detail, a summary of the frequency distributions for the variables presented. The response accurately and clearly explains, in detail, the number of times the value occurs in the data. The response accurately and clearly explains, in detail, the appearance of the data, the range of data values, and an explanation of extreme values in describing intervals that sufficiently provides an analysis that fully supports the categorization of each variable value. The response includes relevant, specific, and appropriate examples that fully support the explanations provided for each of the areas described. 28 (28%) – 31 (31%) The response accurately summarizes the frequency distributions for the variables presented. The response accurately explains the number of times the value occurs in the data. The response accurately explains the appearance of the data, the range of data values, and explains extreme values in describing intervals that provides an analysis which supports the categorization of each variable value. The response includes relevant, specific, and accurate examples that support the explanations provided for each of the areas described. 25 (25%) – 27 (27%) The response inaccurately or vaguely summarizes the frequency distributions for the variables presented. The response inaccurately or vaguely explains the number of times the value occurs in the data. The response inaccurately or vaguely explains the appearance of the data, the range of data values, and inaccurately or vaguely explains extreme values. An analysis that may support the categorization of each variable value is inaccurate or vague. The response includes inaccurate and irrelevant examples that may support the explanations provided for each of the areas described. 0 (0%) – 24 (24%) The response inaccurately and vaguely summarizes the frequency distributions for the variables presented, or it is missing. The response inaccurately and vaguely explains the number of times the value occurs in the data, or it is missing. The response inaccurately and vaguely explains the appearance of the data, the range of data values, and an explanation of extreme values, or it is missing. An analysis that does not support the categorization of each variable values is provided, or it is missing. The response includes inaccurate and vague examples that do not support the explanations provided for each of the areas described, or it is missing. Summarize your interpretation of the descriptive statistics provided in the output for respondent’s age, highest school grade completed, race and ethnicity, currently employed, and family income from prior month. 45 (45%) – 50 (50%) The response accurately and clearly summarizes in detail the interpretation of the descriptive statistics provided. The response accurately and clearly evaluates in detail each of the variables presented, including an accurate and complete description of the sample size, the mean, the median, standard deviation, and the size and spread of the data. 40 (40%) – 44 (44%) The response accurately summarizes the interpretation of the descriptive statistics provided. The response accurately explains evaluates each of the variables presented, including an accurate description of the sample size, the mean, the median, standard deviation, and the size and spread of the data. 35 (35%) – 39 (39%) The response inaccurately or vaguely summarizes the interpretation of the descriptive statistics provided. The response inaccurately or vaguely evaluates each of the variables presented, including an inaccurate or vague description of the sample size, the mean, the median, the standard deviation, and the size and spread of the data. 0 (0%) – 34 (34%) The response inaccurately and vaguely summarizes the interpretation of the descriptive statistics provided, or it is missing. The response inaccurately and vaguely evaluates each of the variables presented, including an inaccurate and vague description of the sample size, the mean, the median, the standard deviation, and the size and spread of the data, or it is missing. Written Expression and Formatting – Paragraph Development and Organization: Paragraphs make clear points that support well-developed ideas, flow logically, and demonstrate continuity of ideas. Sentences are carefully focused—neither long and rambling nor short and lacking substance. A clear and comprehensive purpose statement and introduction is provided which delineates all required criteria. 5 (5%) – 5 (5%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity. A clear and comprehensive purpose statement, introduction, and conclusion is provided which delineates all required criteria. 4 (4%) – 4 (4%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity 80% of the time. Purpose, introduction, and conclusion of the assignment is stated, yet is brief and not descriptive. 3 (3%) – 3 (3%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity 60%–79% of the time. Purpose, introduction, and conclusion of the assignment is vague or off topic. 0 (0%) – 2 (2%) Paragraphs and sentences follow writing standards for flow, continuity, and clarity < 60% of the time. No purpose statement, introduction, or conclusion was provided. Written Expression and Formatting – English writing standards: Correct grammar, mechanics, and proper punctuation 5 (5%) – 5 (5%) Uses correct grammar, spelling, and punctuation with no errors. 4 (4%) – 4 (4%) Contains a few (1 or 2) grammar, spelling, and punctuation errors. 3 (3%) – 3 (3%) Contains several (3 or 4) grammar, spelling, and punctuation errors. 0 (0%) – 2 (2%) Contains many (≥ 5) grammar, spelling, and punctuation errors that interfere with the reader’s understanding. Written Expression and Formatting – The paper follows correct APA format for title page, headings, font, spacing, margins, indentations, page numbers, parenthetical/in-text citations, and reference list. 5 (5%) – 5 (5%) Uses correct APA format with no errors. 4 (4%) – 4 (4%) Contains a few (1 or 2) APA format errors. 3 (3%) – 3 (3%) Contains several (3 or 4) APA format errors. 0 (0%) – 2 (2%) Contains many (≥ 5) APA format errors. Total Points: 100 Name: Assignment Rubric
Turn the brief into deliverables
- 01SPSS output for all three measures of centre.
- 02An interpretation of where they diverge and what that implies.
- 03A justified choice of which centre to report as the summary.
- 04A note on any variable where a measure is not meaningful.
Produce, inspect, then explain the divergence
The variables and their shapes
Present each variable with all three centres and an initial read on shape.
Where the measures diverge
Identify skew and possible bimodality from the divergences.
Choosing what to report
Select a summary measure and justify it against the claim being made.
Where a measure fails
Note variables for which one or more measures is uninterpretable.
Choosing a centre when the distribution is not symmetric
Recommended databases
- StatPearls statistics chapters
- Your SPSS materials
- OpenStax Introductory Statistics
- PubMed Central
Search sequence
- 1.Look up how mean-median divergence signals skew and in which direction.
- 2.Check how your software reports multiple modes before trusting the value.
- 3.Find a published paper reporting a skewed clinical variable and note which centre it used.
- 4.Read on bimodality as evidence of a mixed population.
Reference shortlist
These are authoritative starting points, not a ready-made bibliography. A qualified reviewer must confirm that each source fits the assignment and supports the claim beside which it is cited.
Nothing here is cleared for citation until you have read it.
- 01
Exploratory Data Analysis: Frequencies, Descriptive Statistics, Histograms, and Boxplots
StatPearls, NCBI Bookshelf · 2023
Covers centre, spread and the graphical checks that reveal skew, which is what the three measures are being compared to detect.
- 02
Epidemiology Morbidity And Mortality
StatPearls, NCBI Bookshelf · 2023
Shows how summary measures are chosen and reported for health data with awkward distributions.
- 03
Study Bias
StatPearls, NCBI Bookshelf · 2023
Explains how an unexamined distribution introduces bias into every later comparison.
- 04
13.1 One-Way ANOVA
OpenStax, Introductory Statistics 2e · 2023
Shows what the later comparison of group means assumes about the distributions summarised here.
Review before submission
Common mistakes
- Reporting all three and commenting on none.
- Treating the mean as always the right summary regardless of shape.
- Interpreting a mode on a continuous variable.
- Missing the SPSS footnote when multiple modes exist.
Submission checklist
- Have you said what the mean-median relationship implies?
- Is your choice of summary tied to a stated claim?
- Did you check for multiple modes?
- Have you flagged any measure that should not be interpreted?
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