How to Calculate Standard Deviation on a BA II Plus (Sample & Population)

In this tutorial

Sample vs population: which symbol is which
Entering data with the DATA worksheet
Example 1: sample standard deviation of exam scores
Example 2: a cleaner dataset where you can verify by hand
Single-variable (1-V) mode for one-column data
Common mistakes and error traps

Sample vs population: Sx and σx

Both answers come from the same numbers; they differ only in the denominator:

Sx — sample standard deviation. Uses n − 1 in the denominator. Use it when your numbers are a sample of a larger population (most exam questions).
σx — population standard deviation. Uses n. Use it only when the dataset really is the whole population.

With a handful of data points the two differ noticeably; with large n they converge. The CFA curriculum asks for the sample version almost every time — but always read the stem.

Entering data with the DATA worksheet

Press [2nd] then [7] (DATA).
Press [2nd] then [CLR WORK] to clear old entries.
At X01=, type the first number, press [ENTER].
Press ↓ to Y01, enter 1 as a placeholder (or skip with ↓), then ↓ again for X02.
Enter every value the same way.

For single-column data, switch to 1-V mode first so you do not need Y placeholders: press [2nd] then [8] (STAT), then [2nd] then [SET] until 1-V appears, then return to DATA with [2nd] then [7]. In 1-V mode each [ENTER] accepts one value and moves straight to the next X.

Example 1: sample standard deviation of exam scores

Five students scored 85, 92, 78, 95 and 88. Compute the sample standard deviation.

Press [2nd] then [7], then [2nd] then [CLR WORK].
Enter 85 [ENTER], 92 [ENTER], 78 [ENTER], 95 [ENTER], 88 [ENTER] (1-V mode).
Press [2nd] then [8] (STAT).
Read n=5 and x̄=87.6 — the mean.
Scroll down to Sx=, read 6.58 — the sample standard deviation.
Scroll down to σx=, read 5.89 — the population version.

Verify the sample number: the five deviations from 87.6 are −2.6, 4.4, −9.6, 7.4, 0.4; their squares sum to 173.2; dividing by n−1 = 4 gives 43.3; √43.3 = 6.58. The calculator agrees.

Example 2: a symmetric dataset for hand verification

Eight returns (in percent): 2, 4, 4, 4, 5, 5, 7, 9. This set is built so the arithmetic is clean.

Clear DATA: [2nd] then [7], [2nd] then [CLR WORK].
Enter the eight values.
Press [2nd] then [8] and scroll to the standard-deviation lines:

x̄= — 5.00 (the mean is symmetric)
Sx= — 2.14 (sample: √(32/7))
σx= — 2.00 (population: √(32/8))

Hand check: deviations from 5 are −3, −1, −1, −1, 0, 0, 2, 4; squared they sum to 9+1+1+1+0+0+4+16 = 32. Sample divides by 7 → √(32/7) ≈ 2.14. Population divides by 8 → √4 = 2. Exactly what the calculator shows.

Which one do exam questions want?

Phrases like "the sample standard deviation of returns" or "using n − 1" → Sx.
Phrases like "the population standard deviation" or "the standard deviation of the entire market" → σx.
No qualifier at all → default to Sx, then re-read the question.

Statistics theory (variance, covariance, correlation) is covered in the advanced functions tutorial; this page is the pure "which key gives the number" routine.

Common mistakes and error traps

Reading Sx when the question asks for σx — the most expensive 0.1-second mistake in the exam room. Check the label on the display, not the position.
Leftover data. Forgetting [2nd] then [CLR WORK] silently mixes the new dataset with the old one.
Y placeholders polluting the dataset. In LIN mode, every pair counts; a stray 1 in a Y01 slot skews the sums. Use 1-V mode for single-column data.
Wrong mode remembered. The calculator keeps the last regression type; confirm 1-V or LIN before entering data.
Error 2 on an empty dataset. Pressing [CPT] with no data triggers the statistics error — see the error-code guide for the full list.