Organising data & statistical charts · Ages 12–13
Drawing stem-and-leaf diagrams and histograms
Keep empty stems; bars run boundary to boundary.
How to do it
Method
Keep empty stems; bars run boundary to boundary
Data 41, 43, 62: stems 4, 5, 6, stem 5's row empty
Another way
Sort the data first
41, 43, 62 → 4 | 1 3, 6 | 2
In full
To draw a stem-and-leaf diagram: find the least and greatest values, write every stem from smallest to largest, including a stem with no data (its row left empty); write each value's leaf beside its stem, then put each row's leaves in order and add a key (such as 4 | 5 = 45). Or sort the data first and write the leaves in turn, with nothing to reorder. To draw a histogram: make the grouped frequency table and find each class's boundaries; mark the boundaries on the horizontal axis, draw each bar from its lower boundary to its upper one, the bars touching; each bar's height is its class's frequency, on a vertical scale from 0 in equal steps. Check: the number of leaves, and the bars' heights added, both equal the number of data.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A stem-and-leaf diagram of these data, the tens digit as the stem: 53, 15, 23, 53, 28, 46. Counting from the smallest stem to the largest, how many stems are written?
Show the answer and working
Answer: 5
Least 15, greatest 53: stems 1 to 5, writing those with no data too, 5 − 1 + 1 = 5 stems.
Example 2
The table is drawn as a histogram (the left column is scores, the right players). The bar for 30–39 runs along the axis from to , and is tall.
Fill in each blank
Show the answer and working
Answer: 29.5, 39.5, 12
The bar runs from the lower boundary 29.5 to the upper 39.5, as tall as the frequency 12.
Example 3
These 8 values go in a stem-and-leaf diagram, the tens digit as the stem: 42, 57, 47, 24, 50, 45, 40, 23. Stem 2's row has 3 leaves.
True or false?
Show the answer and working
Answer: False
Count the values with tens digit 2: 2, so stem 2's row has 2 leaves.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Here are 8 values: 53, 36, 41, 26, 42, 48, 20, 42. Which stem-and-leaf diagram shows them correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
2.A stem-and-leaf diagram of these data, the tens digit as the stem: 77, 26, 39, 11, 52, 66. Counting from the smallest stem to the largest, how many stems are written?
Answer:
3.Data grouped as 60–69, 70–79, … are drawn as a histogram. At which two values on the horizontal axis are the first bar's edges?
- A. 64.5、74.5
- B. 60、69
- C. 59.5、69.5
- D. 60、79
Choose the right answer
Answer:
4.These 8 values go in a stem-and-leaf diagram, the tens digit as the stem: 54, 20, 49, 36, 57, 58, 32, 47. Stem 3's row has 3 leaves.
True or false?
Answer:
5.Here are 8 players' heights in cm: 146, 168, 167, 149, 153, 149, 179, 156. With the first two digits as the stem and the units as the leaf, which stem-and-leaf diagram is right?
- A
- B
- C
- D
Choose the right picture
Answer:
All the answers
- 1. C
- 2. 7
- 3. C. 59.5、69.5
- 4. False
- 5. D
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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