At Core tier, data is always given as a list or an ungrouped frequency table — never grouped into class intervals.

The median is the middle value once the data is ordered (or the average of the two middle values, for an even count). The mode is the most frequent value.

Worked example. The number of books read last month by 7 students was $2, 2, 2, 4, 5, 6, 7$. Find the mean, median, mode and range.

Ordered already, $n=7$. Mode $= 2$ (appears 3 times). Median $=$ the 4th value $= 4$.

When data is grouped by frequency rather than listed individually, each value must be multiplied by how often it occurs before summing, since simply adding the distinct values would ignore how many times each one actually appeared.

Worked example. The table shows the number of pets owned by 20 students. Find the mean number of pets.

Mean uses every value and is best for an overall typical value, but is dragged by extreme outliers. Median is unaffected by outliers, since it only depends on position, not size. Mode is the only average that works for non-numerical (categorical) data, and is useful when the most popular value matters more than a typical one.

Worked example. A small company's salaries (in thousands) are $22, 24, 25, 26, 90$. Explain why the median is a better measure of a "typical" salary here than the mean.

The mean ($37.4$) is pulled upward by the single outlier of $90$, so it doesn't represent what most employees actually earn. The median ($25$) is unaffected by that one extreme value and better reflects a typical salary in this data set.