What is the difference between sigma x and s x?

Sigma x is population standard deviation using divisor n. The s x result is sample standard deviation using divisor n minus one.

Why do I get a different answer from a textbook?

The most common reason is selecting population SD when the exercise asks for sample SD, or the reverse.

Can the Casio frequency column handle repeated data?

Yes on supported ES models when frequency display is enabled. Enter each distinct value once and its count in the FREQ column.

Standard Deviation on Casio fx-991ES and fx-991MS

Use one-variable STAT mode on fx-991ES models or SD mode on fx-991MS models, enter the data, then select σx for population SD or sx for sample SD.

Checked against official Casio manuals · Last reviewed: August 22, 2026 · Key labels vary by regional edition

Choose the correct result

σx = population SD · sx = sample SD

If your answer differs from a textbook, first check whether the problem expects division by n or by n − 1.

Casio fx-991ES and fx-991ES Plus steps

Press MODE and choose STAT.
Select 1-VAR for one-variable data.
Enter each observation in the X column, pressing equals after each entry.
Open the STAT calculation menu, choose Var, then select σx for population SD or sx for sample SD.

On the ES Plus family, Casio’s STAT editor can also display a FREQ column. Exact menu numbers differ between editions, so follow the labels rather than memorizing only a numeric shortcut.

Casio fx-991MS steps

Press MODE until the mode list appears, then choose SD.
Clear old statistical memory with the calculator’s CLR → Scl sequence before a new data set.
Enter each value using the DT data-entry function. Repeated values can be entered repeatedly or with the frequency syntax described in the manual.
Open S-VAR and choose σx for population SD or sx for sample SD.

The fx-991MS does not use the same table-style editor as the ES family. This is why instructions written for an fx-991ES can appear not to work on an fx-991MS.

Standard deviation with a frequency table

On an ES Plus model with FREQ enabled, enter each distinct x value once and put its count in the FREQ column. This is equivalent to typing that x value repeatedly. For class intervals, first replace each interval with its midpoint; the resulting SD is an estimate because the raw values are unknown.

For a full working table, use the grouped-data standard deviation calculator.

How to check your Casio result

For the values 1, 2, and 3, the mean is 2. Population SD is √(2 ÷ 3) ≈ 0.81649658, while sample SD is √(2 ÷ 2) = 1. Enter this short data set first. If σx gives about 0.8165 and sx gives 1, the mode and result choice are correct.

Before every new set: remove or clear earlier observations. Old values left in statistical memory are a common source of wrong answers.

Frequently asked questions

What is the difference between σx and sx?

σx is population standard deviation using n. sx is sample standard deviation using n − 1.

Why is my answer different from the book?

Check sample versus population choice, old data in memory, frequency entries, and whether grouped intervals require midpoints.

Are fx-991ES and fx-991MS keystrokes identical?

No. ES models use a STAT editor, while MS models use SD mode and DT-style data entry.

Can I enter frequencies?

Yes, with the FREQ column on supported ES models or the frequency entry procedure in the relevant MS manual.