Sample quantile
Definition taught in Descriptive statistics, part of Data analysis
Sample quantile
| Type | Definition |
| Taught in | Descriptive statistics |
| Part | Data analysis |
| Worked examples | 1 |
| Questions using it | 1 |
A sample p-quantile, for 0<p<1, is a value q_p such that a fraction p of the data is at most q_p. The 0.25, 0.5 and 0.75 quantiles are the first quartile, the median and the third quartile; the p-quantile is also the 100pth percentile.
Examples
The ages of 299 patients
Worked example from Descriptive statistics
Question. Summarise the patients’ ages.
Solution.
mean(heart$age); median(heart$age) # 60.83 60
quantile(heart$age, c(0.25, 0.75)) # 51 70
IQR(heart$age) # 19
sd(heart$age) # 11.89
range(heart$age) # 40 95The patients are aged 40 to 95. The mean and median are close, 60.8 and 60, so the ages are roughly symmetric. The middle half lies between 51 and 70, an interquartile range of 19 years, and the standard deviation is 11.9 years. For a roughly normal sample the interquartile range is about 1.35 standard deviations; here 19/11.9=1.6, so the ages are a little flatter than normal.
Used in
- Taught in Descriptive statistics, where the derivation and examples are.
- Also used in Statistical inference · Regression examples
- Questions that use it (1) — Summaries of ten cartons
- All 2 questions on Descriptive statistics
See also
Five-number summary and boxplot · Interquartile range · Sample variance and standard deviation · Normal quantile plot