Stem-and-leaf plots, box plots and misleading graphs
Mathematics Prep 1 Term 1, Unit 3, Lesson 1
GoalMake and read a stem-and-leaf plot, find quartiles, draw a box plot and spot a misleading graph.
New words
stem-and-leaf plot · a table that splits each number into a stem (tens) and a leaf (units)quartiles · values that cut the ordered data into four equal partsbox plot · a picture of the minimum, Q1, median, Q3 and maximumkey · a note that says how to read the stems and leaves
Explanation
A stem-and-leaf plot keeps every value: the stem holds the tens and the leaf holds the units, so 2 | 3 means 23. Always sort the leaves and write a key. The median is the middle value of the ordered data. The first quartile Q1 is the median of the lower half and the third quartile Q3 is the median of the upper half; with an odd number of values, the median is left out of both halves. A box plot draws five numbers: minimum, Q1, median, Q3 and maximum, with a box from Q1 to Q3. It hides the single values. Be careful with graphs that start the axis above zero: they make small differences look large.
Key: 2 | 3 means 23
Stem
Leaves
1
2 5 7
2
1 3 4 8
3
1 3 6
4
0
Worked examples
Eleven scores in order: 12, 15, 17, 21, 23, 24, 28, 31, 33, 36, 40. Stems are the tens: 1, 2, 3, 4. Leaves are the units. The plot is shown, and 2 | 3 means 23. Check: 3 + 4 + 3 + 1 = 11 leaves.
Median and quartiles. The 6th value is the median: 24. The lower half is 12, 15, 17, 21, 23, so Q1 is its middle value, 17. The upper half is 28, 31, 33, 36, 40, so Q3 = 33. The minimum is 12 and the maximum is 40.
Misleading graph. Two shops sell a bag for 42 LE and 44 LE. The first graph starts its axis at 40, so shop B looks twice as tall as shop A (4 against 2). The real prices are almost equal. A graph that starts at 0 shows this honestly.
Class activity
Graph detective. With a grown-up, find a graph in a newspaper or on a shop poster. Does the axis start at zero? Do the columns have equal widths? Explain what you would change to make it honest.
Practice
1
Make a stem-and-leaf plot for 31, 24, 35, 22, 28, 31.
