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How to find standard deviation on a Casio calculator

Switch to statistics mode, enter each value, then open the one-variable results. Read sx for a sample or σx for a population — older models label them xσn−1 and xσn. The exact keys depend on which family your calculator belongs to.

Which Casio do you have?

FamilyModelsHow to tellSample / population label
ClassWiz CWfx-991CW, fx-570CW, fx-83GT CW, fx-85GT CWA HOME key, an OK key and an EXE keysx / σx
ClassWiz EXfx-991EX, fx-570EXA MENU key opens a grid of app iconssx / σx
ES PLUS and GT PLUSfx-991ES PLUS, fx-115ES PLUS, fx-570ES PLUS, fx-83GT PLUS, fx-85GT PLUSNatural textbook display, a MODE key, no MENUsx / σx
MSfx-82MS, fx-85MS, fx-300MS, fx-350MS, fx-570MS, fx-991MSTwo-line display; M+ is also labelled DTsx / σx (older printings: xσn−1 / xσn)
Graphingfx-CG50 and similarColour graphing screen, F1–F6 keyssx / σx

Every sequence below is taken from Casio's own user's guide for that model, listed under sources at the end of the page. Numbers in brackets are the menu item to press, with its on-screen name after it.

Casio fx-991CW, fx-570CW and fx-83GT / 85GT CW

  1. Open Statistics. Press HOME, select the Statistics icon and press OK. Select 1-Variable and press OK. A table with an x column opens.
  2. Enter the data. Type each value and press EXE.
  3. Open the results. Press OK, select 1-Var Results and press OK.
  4. Read the answer. The first screen shows x̄ and σx (population); press ▼ to reach sx (sample) and n. Press AC to go back to the table.

Casio fx-991EX and fx-570EX

  1. Open Statistics. Press MENU, select the Statistics icon and press =. Press 1 (1-Variable). A table with an x column opens.
  2. Enter the data. Type each value and press =.
  3. Open the results. Still in the table, press OPTN 3 (1-Variable Calc). If you pressed AC first, the same item is OPTN 2.
  4. Read the answer. σx is the population standard deviation and sx the sample one, with x̄ and n in the same list.

Casio fx-991ES PLUS, fx-115ES PLUS and fx-83GT / 85GT PLUS

  1. Open STAT mode. ES PLUS: MODE 3 (STAT). GT PLUS: MODE 2 (STAT). Then press 1 (1-VAR).
  2. Enter the data. Type each value and press =.
  3. Leave the table. Press AC.
  4. Show the result. Press SHIFT 1 (STAT) 4 (Var), then 4 (sx) for the sample standard deviation or 3 (σx) for the population one, and press =. In the same menu, 1 is n and 2 is x̄.

Casio fx-82MS, fx-350MS, fx-570MS and fx-991MS

  1. Open SD mode. fx-82MS, fx-85MS, fx-300MS and fx-350MS: MODE 2 (SD). fx-570MS and fx-991MS: MODE MODE 1 (SD).
  2. Clear old data. Press SHIFT MODE (CLR) 1 (Scl) =. Skipping this is the usual cause of a wrong answer: SD mode keeps the last problem's values.
  3. Enter the data. Type each value and press M+, which acts as the DT (data) key in SD mode.
  4. Show the result. Press SHIFT 2 (S-VAR), then 3 (sx) for the sample standard deviation or 2 (σx) for the population one, and press =. 1 in the same menu is x̄. Older printings label the two xσn−1 and xσn.

Casio graphing calculators (fx-CG50 and similar)

  1. Open Statistics. Press MENU and choose Statistics.
  2. Enter the data. Type the values into List 1, pressing EXE after each.
  3. Calculate. Press F2 (CALC), then F1 (1-VAR). The results list σx and sx, with x̄ and n above them.

Entering a frequency table

When the data arrives as values with counts — a score of 7 that occurred 4 times — enter each value once with its frequency rather than typing it four times:

  • ClassWiz CW: in the table, press TOOLS and select Frequency → On, then AC to return. A Freq column appears.
  • ClassWiz EX: SHIFT MENU (SETUP) ▼ 3 (Statistics) 1 (On), then open Statistics as usual. A Freq column appears.
  • ES PLUS: SHIFT MODE (SETUP) ▼ 4 (STAT) 1 (ON). GT PLUS: the same STAT ON setting is on the SETUP menu (SHIFT MODE). A FREQ column appears.
  • MS: type the value, then SHIFT , (the ; symbol), then the frequency, then M+. For example 7 ; 4 M+ enters 7 four times.

Changing the frequency setting clears the data already in the table, so switch it on before you start typing. For class intervals such as 10–19, enter each midpoint as the value. The result is then an estimate; the grouped data calculator explains how far off it can be.

When the answer looks wrong

  • Wrong one of the two. sx is always larger than σx. If your answer is slightly too big or too small, you probably read the other one.
  • Leftover data. Check that n in the results matches the number of values you meant to enter. MS models keep old data until you clear it with SHIFT MODE (CLR) 1 (Scl) =; on ClassWiz CW, TOOLS → Edit → Delete All empties the table.
  • Only one value. The sample formula divides by n − 1, so sx needs at least two values.
  • Frequency column switched on by accident. Every Freq cell defaults to 1, but a stray 0 or 2 changes the result. Turn the column off if you do not need it.

Check the calculator's answer

Type the same numbers below. The sample result matches sx (xσn−1), and switching to Population matches σx (xσn). Every step of the working is shown if you need to find where a hand calculation went wrong.

Separate numbers with commas, spaces or new lines, or paste a spreadsheet column. Decimals and negatives are fine.

Calculation type

Standard deviation (sample)

3.04432

Your values typically sit about 3.04 above or below their mean of 15.88, in the same units as your data. 5 of 8 values (63%) fall between 12.83 and 18.92, within one standard deviation of the mean; for normally distributed data about 68% would.

Count (n)
8
Mean (x̄)
15.875
Variance (s²)
9.26786
Standard error
1.07633
Minimum
12
Q1 (25%)
13.75
Median
15.5
Q3 (75%)
17.5
Maximum
21
Range
9
More statistics (5)
Relative SD (%RSD)
19.1768%
Coefficient of variation
0.191768
Sum (Σx)
127
Sum of squares, Σ(x − x̄)²
64.875
IQR (Q3 − Q1)
3.75

Data distribution

10 15 20 25 mean 15.88 −1 SD +1 SD 12 — 1.27 SD below the mean15 — 0.287 SD below the mean17 — 0.37 SD above the mean14 — 0.616 SD below the mean19 — 1.03 SD above the mean21 — 1.68 SD above the mean16 — 0.0411 SD above the mean13 — 0.944 SD below the mean Value

Shaded bands mark ±1, ±2 and ±3 SD from the mean. 5 of 8 values (63%) fall within ±1 SD.

Chart as text

Mean 15.875, sample standard deviation s = 3.04432, from 8 values between 12 and 21.

  • Within ±1 SD (12.83 to 18.92): 5 of 8 values (63%). About 68% for normal data.
  • Within ±2 SD: 8 (100%). About 95% for normal data.
  • Within ±3 SD: 8 (100%). About 99.7% for normal data.
Show the working, step by step

Sources

Key sequences are taken from Casio's user's guides:

Common questions

Which value on a Casio calculator is the standard deviation?

Casio shows two. sx (or xσn−1 on older MS printings) is the sample standard deviation, which divides by n − 1. σx (or xσn) is the population standard deviation, which divides by n.

If the question says "sample", or does not say, use sx.

What is SD mode on a Casio calculator?

On the fx-82MS family and other MS models, SD is the name of the statistics mode: Standard Deviation mode, reached with MODE 2 (or MODE MODE 1 on the fx-570MS and fx-991MS). In it the M+ key stops adding to memory and becomes the data-entry key, labelled DT. Newer models call the same thing STAT or Statistics.

Why can my Casio not give sx for a single value?

The sample standard deviation divides by n − 1, which is zero when n = 1, so it cannot be calculated and the calculator reports an error. Enter at least two values, or read σx if the single value really is the whole population.

Why does my Casio give a different answer from the textbook?

Almost always one of two things: you read σx where the book wanted sx (or the reverse), or values from a previous problem were still in the data table. Check the count n in the results against the number of values you meant to enter.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.