Variability

Variability is how much values differ, and the word covers two things that are measured with two different numbers. Inside one data set it is the spread of the observations, reported by the standard deviation $s$ or the interquartile range. Across repeated samples from the same population it is sampling variability, the bounce in a statistic such as $\bar{x}$ (x-bar) from one sample to the next, reported by a standard error.

Two classes both average 75 on a test. Class A scored 71, 73, 75, 77, 79 and Class B scored 55, 65, 75, 85, 95. The means are identical, $375/5 = 75$ in each. The sums of squared deviations are 40 and 1000, so $s = \sqrt{40/4} = 3.16$ against $s = \sqrt{1000/4} = 15.81$. A center on its own describes neither class, which is why a description always names variability alongside it.

The second kind shrinks with sample size. If individual measurements have $\sigma = 12$, the sample mean from $n = 4$ has standard deviation $12/\sqrt{4} = 6$, and from $n = 36$ it is $12/\sqrt{36} = 2$. Nine times the data, one third of the bounce.

That is where "a bigger sample has less variability" goes wrong. A larger sample does not make the individuals more alike, and $\sigma$ is a property of the population that no sample size touches. What shrinks is the variability of the statistic computed from the sample. Say which of the two you mean, because the first claim is false and the second is the foundation under every confidence interval in the course.

Low variability is also not accuracy. An estimator can land in nearly the same place every time and still land in the wrong place every time, which is bias rather than variability, and a bigger sample does not fix it. Variability is the width of the pattern on the target; bias is where the pattern is centered. Both have to be small before an estimate is worth anything.