Descriptive Statistics: Summarizing Your Data
Understand mean, median, mode, standard deviation, and how to describe the shape of your data distribution before running any inferential test.
You'll learn
How to summarize your dataset with mean, median, SD, and IQR.
Use this when
You want to understand your data before running statistical tests.
What Are Descriptive Statistics?
Descriptive statistics summarize and describe the main features of a dataset. Unlike inferential statistics (which make conclusions beyond your sample), descriptive statistics only describe what you have. Every research paper begins with a "Table 1" of descriptive statistics.
Measures of Central Tendency
Central tendency describes where the "center" of your data lies. The three main measures are mean, median, and mode.
Mean (Average)
The mean is the sum of all values divided by the number of values. It is the most commonly used measure, but it is sensitive to extreme values (outliers).
Mean (x̄) = (Σxᵢ) / n
Example: Blood glucose values 95, 102, 98, 110, 87 → Mean = (95+102+98+110+87)/5 = 98.4 mg/dL
Median (Middle Value)
The median is the middle value when data is sorted. It is robust to outliers, making it preferable for skewed distributions (e.g., income, hospital length of stay).
Example: Income values $30k, $35k, $40k, $42k, $500k → Median = $40k. The mean ($129.4k) is misleading because of the outlier.
Mode (Most Frequent)
The mode is the value that appears most often. It is the only valid measure of central tendency for nominal data. Data can be unimodal (one mode), bimodal (two modes), or multimodal.
Measures of Spread (Variability)
Two datasets can have the same mean but very different distributions. Measures of spread tell you how much values vary around the center.
Standard Deviation (SD)
SD measures the average distance of data points from the mean. A small SD means values cluster tightly; a large SD means values are spread out.
SD = √[ Σ(xᵢ - x̄)² / (n-1) ]
- ●Report as: Mean ± SD (e.g., Age: 45.2 ± 8.3 years)
- ●Use when data is approximately normally distributed
- ●Mean ± 1 SD covers ~68% of normally distributed data
- ●Mean ± 2 SD covers ~95% of normally distributed data
Interquartile Range (IQR)
The IQR is the range from the 25th percentile (Q1) to the 75th percentile (Q3). It is robust to outliers, and should be paired with the median for skewed data.
Report as: Median [IQR] or Median (Q1–Q3). Example: Length of stay: 4 days [IQR: 2–8].
Distribution Shape: Skewness and Kurtosis
Before choosing which summary statistics to report, check the shape of your distribution.
- ●Symmetric / Normal → Use mean ± SD
- ●Right-skewed (long tail to the right, e.g., income, survival time) → Use median [IQR]
- ●Left-skewed (long tail to the left) → Use median [IQR]
- ●Kurtosis: describes "peak-ness" — high kurtosis means more extreme outliers than a normal distribution
How to Report Descriptive Statistics
In research papers, descriptive statistics are typically presented in "Table 1: Baseline Characteristics." Use these rules:
- 1.Continuous, normally distributed → Mean ± SD
- 2.Continuous, skewed → Median [IQR] or Median (Min–Max)
- 3.Categorical → n (%) for each category
- 4.Always state the sample size (N) and missing data counts
Practice with your own dataset
Upload any dataset and run Descriptive Statistics to see mean, median, SD, IQR, and distribution info for all your numeric variables at once.
- 1.Go to Analyze and upload your dataset
- 2.Select "Descriptive Statistics"
- 3.Choose the numeric variables you want to summarize
- 4.Review mean, median, SD, min, max, and skewness for each variable
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Further reading
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