SL 4.3—Mean, median, and mode

The mean is $\bar{x}=\frac{\sum x}{n}$.

$6+9+11+14+20=60$.

$n=5$, so $\bar{x}=\frac{60}{5}=12.0$.

The mean is $12.0$.

$11.0$ is the median of the sorted data, not the mean.

$14.0$ mistakenly uses the middle value from an incorrect count.

$13.5$ results from dividing 60 by 4.44 or a similar arithmetic slip in the denominator.

Only $12.0$ correctly sums and divides by $n=5$.

Ascending order: 15, 18, 19, 22, 25, 30.

$n=6$ (even), so median is the average of 3rd and 4th values.

Middle values are 19 and 22: $\frac{19+22}{2}=21.5$.

The median is $21.5$.

$20.5$ comes from wrongly averaging 18 and 23 due to a sorting error.

$19.0$ picks only the 3rd value, forgetting to average with the 4th for even $n$.

$22.0$ picks only the 4th value, forgetting to average with the 3rd.

Only $21.5$ correctly averages both middle values after sorting.