Mean, median and sample standard deviation
Used on the ASP and CSP. The worked example below is computed by code and checked against the source.
Mean = Σx ÷ n
s = √(Σ(x − mean)² ÷ (n − 1))
The median is the middle value of the sorted data (the average of the two middle values when n is even).
Worked example
Data: 2, 4, 4, 4, 5, 5, 7, 9.
mean = 40 ÷ 8 = 5; median = 4.5; s = √(32 ÷ 7) = 2.14
Where it appears on the exam
ASP: ASP11 Domain 1, Mathematical Calculations
Blueprint: ASP11 Domain 1, task 11: descriptive statistics
Practice: Statistics and Probability
CSP: CSP11 Domain 2, Program Management
Blueprint: CSP11 Domain 2, task 14: analyze and/or interpret data (mean, median, mode)
Practice: Incident and DART Rate Calculations
Source
The formula comes from
NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.1 Measures of Location and 1.3.5.6 Measures of Scale(opens itl.nist.gov in a new tab)“mean - the mean is the sum of the data points divided by the number of data points. ... median - the median is the value of the point which has half the data smaller than that point and half the data larger than that point. ... standard deviation - the standard deviation is the square root of the variance.”
Questions
- What is the formula for mean, median and sample standard deviation?
- Mean = Σx ÷ n; s = √(Σ(x − mean)² ÷ (n − 1)). The median is the middle value of the sorted data (the average of the two middle values when n is even).
- Will this formula be given on the BCSP exam?
- BCSP says the formula is included in the question whenever one is needed, unless the question is testing whether you know the formula. You can't bring a formula sheet into the exam, so learn what each formula does and when to use it.
BCSP on formulas at the exam
BCSP, What to Expect When Sitting for a BCSP Exam (item 7)(opens bcsp.org in a new tab)“For any question requiring a mathematical formula, the formula will be included within the exam question (unless the question is specifically testing your knowledge of a formula). You will not be provided or permitted to bring a formula sheet.”
Related
- Fault tree gates (independent events)
- Force from mass and deceleration
- Unit conversions
- ASP formula sheet
- CSP formula sheet
Checked 2026-10-16. Spot a problem? Email hello@passcited.com.