How Do You Calculate Standard Deviation and Variance Using Technology?

Use your GDC's one-variable statistics function to enter the data and calculate the population standard deviation, usually displayed as $\sigma_x$. The variance is its square: $\text{variance}=\sigma_x^2$.

GDC Method

The exact menu names depend on your calculator, but the mathematical procedure is the same:

1. Enter the data values into a statistics list, such as List 1.
2. Select one-variable statistics and specify the correct data list.
3. If frequencies are given, enter them in a second list and select that list as the frequency list.
4. Read the population standard deviation $\sigma_x$.
5. Calculate the variance using $\sigma_x^2$.

For a frequency table, do not type each value repeatedly. Enter each distinct value once and place its frequency in the frequency list. Check that the total frequency shown by the GDC equals the number of observations; this catches list-selection and data-entry errors before you record the answer.

For the data $2,4,4,4,5,5,7,9$, the GDC gives:

$$\bar{x}=5,\qquad \sigma_x=2$$

Therefore,

$$\text{variance}=\sigma_x^2=2^2=4.$$

The standard deviation is $2$, while the variance is $4$. Standard deviation has the same units as the original data; variance has squared units.

A common misconception is reading $s_x$ automatically. In IB Mathematics: Applications and Interpretation SL, a supplied data set is treated as the population unless otherwise stated, so use $\sigma_x$, not $s_x$.

Exam Technique

This is SL 4.3: Mean, median, and mode, specifically measures of dispersion, and it can appear on either GDC-active paper. Write down the correct statistic, identify whether it is population or sample, square the standard deviation for variance, and avoid premature rounding by using the full GDC value until the final answer.