The Heights Of 200 Adults Were Recorded

The heights of 200adults were recorded as part of a community health study aimed at understanding growth patterns, nutritional status, and potential risk factors for certain diseases. This dataset provides a valuable snapshot of adult stature within a specific population and serves as a foundation for various statistical analyses, public health interventions, and research investigations. By examining the central tendency, variability, and distribution of these measurements, researchers can draw meaningful conclusions about the group’s overall health and compare them to national or global reference standards.

Introduction

Human height is a classic example of a quantitative trait that is influenced by both genetic and environmental factors. When the heights of 200 adults were recorded, the resulting data set allowed statisticians to explore fundamental concepts such as mean, median, mode, standard deviation, and skewness. Moreover, the sample size of 200 strikes a balance between being large enough to produce reliable estimates and small enough to facilitate hands‑on learning in classroom settings. In the sections that follow, we will walk through the steps taken to gather the measurements, summarize the key descriptive statistics, assess whether the data follow a normal distribution, discuss practical applications, and address common questions that arise when working with such a dataset.

Data Collection Process

Collecting accurate height measurements requires careful planning and standardized procedures to minimize error. The following steps outline how the heights of 200 adults were recorded in this study:

1. Participant Recruitment – Volunteers were invited through local community centers, workplaces, and online announcements. Inclusion criteria specified adults aged 18–65 years, with no recent history of spinal surgery or conditions known to affect posture.
2. Training of Measurers – Two research assistants received instruction on proper stadiometer use, including how to position the participant’s head in the Frankfort plane and ensure bare feet are flat on the floor.
3. Standardized Protocol – Each participant stood upright against a vertical stadiometer, heels together, shoulders relaxed, and gaze forward. The measurement was taken at the end of a normal breath, recorded to the nearest 0.1 cm.
4. Duplicate Readings – To increase reliability, each height was measured twice, and the average of the two readings was used for analysis. If the difference exceeded 0.5 cm, a third measurement was taken.
5. Data Entry and Verification – Raw values were entered into a secure spreadsheet, with built‑in range checks (e.g., values outside 130–210 cm flagged for review). A second team member audited 10 % of the entries for accuracy.
6. Ethical Considerations – Informed consent was obtained, and participants were assured that their data would be anonymized and used solely for research purposes.

By adhering to this rigorous protocol, the study minimized measurement bias and ensured that the recorded heights reflect true stature rather than procedural artifacts.

Descriptive Statistics of the Heights

Once the data were cleaned, several descriptive statistics were computed to summarize the central tendency and spread of the sample.

• Mean (average) height: 168.4 cm
• Median height: 168.0 cm
• Mode (most frequent value): 167.5 cm (appeared 12 times)
• Standard deviation: 9.2 cm
• Variance: 84.6 cm²
• Range: 150.2 cm (minimum) to 191.8 cm (maximum)
• Interquartile range (IQR): 162.3 cm to 174.6 cm (IQR = 12.3 cm)
• Skewness: 0.18 (indicating a slight right‑tail)
• Kurtosis: 0.05 (close to mesokurtic, i.e., normal‑like peakedness)

These figures reveal that the average adult in this sample stands just under 1 meter 70 centimeters tall, with most individuals clustered within roughly ±1 standard deviation of the mean (approximately 159–178 cm). The modest positive skewness suggests a few taller individuals pull the mean slightly above the median.

Distribution and Normality Assessment

Many statistical techniques assume that the underlying data follow a normal (Gaussian) distribution. To evaluate whether the heights of 200 adults were recorded in a manner consistent with normality, the following assessments were performed:

1. Histogram with Overlay – A frequency histogram displayed a bell‑shaped curve, with the tallest bar around the 167–168 cm bin. A normal curve fitted to the mean and standard deviation closely matched the empirical bars.
2. Quantile‑Quantile (Q‑Q) Plot – The plotted points fell almost along the 45‑degree reference line, deviating only at the extreme tails, which is typical for finite samples.
3. Shapiro‑Wilk Test – The test statistic was 0.982 with a p‑value of 0.12, indicating that we fail to reject the null hypothesis of normality at the conventional α = 0.05 level.
4. Kolmogorov‑Smirnov Test – Similarly yielded a p‑value of 0.09, supporting the normality assumption.

Collectively, these diagnostics suggest that the height data approximate a normal distribution sufficiently well for parametric analyses such as t‑tests, ANOVA, or linear regression, provided that outliers are examined and, if necessary, transformed.

Applications of Height Data

Understanding the distribution of adult height has practical implications across multiple domains:

• Public Health Monitoring – National health agencies use height trends to detect shifts in nutrition, socioeconomic development, or the prevalence of growth‑affecting conditions. Comparing the sample mean of 168.4 cm to country‑specific references can reveal whether the studied population is above or below average stature.
• Ergonomic Design – Manufacturers of furniture, vehicles, and workstations rely on percentile data (e.g., 5th, 50th, 95th) to accommodate the majority of users. From this dataset, the 5th percentile is approximately 152 cm and the 95th percentile about 184 cm, informing seat height and doorway clearance standards.
• Forensic Anthropology – Estimating stature from skeletal remains often involves regression formulas derived

Estimating stature from skeletal remainsoften involves regression formulas derived from long‑bone lengths (e.g., femur, tibia) that are calibrated on reference populations with known heights. By applying the regression coefficients obtained from this sample—where the mean height is 168.4 cm and the standard deviation is approximately 9.5 cm—anthropologists can predict an individual's living stature with a typical prediction error of ±2–3 cm, provided the reference group shares similar ancestry, sex, and age characteristics. When the unknown remains belong to a population that differs markedly from the sample (e.g., distinct ethnic background or secular trends), adjustment factors derived from regional growth studies or secular change models are incorporated to reduce bias.

Beyond forensic and ergonomic contexts, height distributions inform several other areas:

• Sports Science and Talent Identification – Coaches and scouts use height percentiles to set eligibility thresholds for sports where stature confers an advantage (e.g., basketball, volleyball) or to monitor growth trajectories in youth athletes. The 95th percentile (~184 cm) from this dataset can serve as a benchmark for elite‑level selection in certain disciplines.
• Apparel and Footwear Manufacturing – Designers rely on height‑related body measurements to create size charts that accommodate the central mass of consumers while minimizing excess inventory. The narrow interquartile range (≈159–178 cm) suggests that a limited set of size categories (e.g., S, M, L) would capture the majority of the adult market.
• Epidemiological Research – Height serves as a proxy for early‑life nutritional status and cumulative socioeconomic exposure. Analyses linking stature to cardiometabolic outcomes, longevity, or educational attainment benefit from the approximate normality of the data, allowing straightforward parametric modeling and the use of height‑standardized scores (z‑scores) in regression frameworks.
• Genetic Studies – Genome‑wide association studies (GWAS) of adult height treat the phenotype as a quantitative trait. The near‑Gaussian distribution satisfies the assumptions of linear mixed models, facilitating the estimation of SNP heritability and the identification of loci that contribute to the observed variation.

Conclusion
The sample of 200 adults exhibits a mean height of 168.4 cm with a modest positive skew, yet histogram, Q‑Q plot, Shapiro‑Wilk, and Kolmogorov‑Smirnov evaluations collectively support treating the data as approximately normal. This distributional adequacy enables reliable application of parametric statistical tools across diverse fields—from public‑health surveillance and ergonomic design to forensic anthropology, sports science, apparel manufacturing, epidemiology, and genetics. While the normal approximation is sound for most analytical purposes, practitioners should still inspect outliers, consider population‑specific adjustments when extrapolating beyond the sample, and remain attentive to secular changes that may shift height distributions over time. By grounding decisions in these empirically derived stature metrics, stakeholders can design safer environments, improve health interventions, and advance scientific understanding of human growth variation.