① Reading a stem and leaf diagramNo calculator
Each value is made from a stem and a leaf. Always check the key. Count carefully to find fractions and percentages of the values.
② Mode, median and interquartile rangeNo calculator
The leaves are in order, so counting through the diagram finds the median. The quartiles are the medians of the lower and upper halves (see Box plots).
③ Mean from a diagramCalculator useful
Read every value, add them up, then divide by how many values there are.
④ Drawing a stem and leaf diagramNo calculator
Order the stems, put the leaves in order in each row, and always add a key.
⑤ Back-to-back diagramsNo calculator
Compare two groups using the median (an average) and the interquartile range (the spread). Read the left side from the stem outwards.
Key steps
Key: always read the key first. It tells you what a stem and leaf stand for.
Ordered diagram: the leaves in each row go from smallest to largest, away from the stem.
Median: count to the middle value. With an even number of values, find halfway between the middle two.
Quartiles: the median splits the data into a lower half and an upper half (leave the median out if there is an odd number of values). \(Q_1\) is the median of the lower half, \(Q_3\) the median of the upper half, and the interquartile range is \(Q_3-Q_1\).
Fractions and percentages: count the values you want, then write the count over the total. Multiply by 100 for a percentage.
Back-to-back: the left-hand leaves are read from right to left, starting next to the stem.