Data and probability · Ages 12–13

Drawing stem-and-leaf diagrams and histograms worksheet

Part of: Organising data & statistical charts

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Data and probability · Ages 12–13

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A stem-and-leaf diagram of these data, the tens digit as the stem: 37, 48, 58, 14, 69, 69. Counting from the smallest stem to the largest, how many stems are written?
Answer:
2.These data go in a stem-and-leaf diagram, the tens digit as the stem: 37, 18, 34, 51, 48, 33. Stem 3's leaves, smallest first, are , , .
Fill in each blank
Answer:
3.The table is drawn as a histogram (the left column is scores, the right players). The bar for 50–59 runs along the axis from to , and is tall.
Fill in each blank
Answer:
4.These 10 values are grouped and drawn as a histogram: 53, 39, 68, 51, 44, 32, 34, 48, 46, 39. How tall is the bar for 30–39?
Answer:
5.These 10 values are grouped as 30–34, 35–39, 40–44, 45–49, 50–54 and drawn as a histogram: 35, 43, 33, 32, 47, 34, 50, 45, 51, 45. The bar for 40–44 runs along the axis from to , and is tall.
Fill in each blank
Answer:
6.The stem-and-leaf diagram (the tens digit as the stem) should show these 8 values, but one is missing: 23, 32, 45, 25, 34, 28, 51, 34. Which value is missing?
Answer:

7.Here are 8 values: 24, 49, 26, 31, 46, 42, 32, 32. Which stem-and-leaf diagram shows them correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
8.Here are 8 values: 45, 33, 45, 23, 37, 44, 25, 38. Which stem-and-leaf diagram shows them correctly?
- A
- B
- C
- D
Choose the right picture
Answer:
9.These 8 values go in a stem-and-leaf diagram, the tens digit as the stem: 33, 31, 26, 51, 23, 44, 25, 27. Stem 3's row has 1 leaves.
True or false?
Answer:
10.Data grouped as 30–39, 40–49, … are drawn as a histogram. At which two values on the horizontal axis are the first bar's edges?
- A. 30、49
- B. 30、39
- C. 29.5、39.5
- D. 34.5、44.5
Choose the right answer
Answer:
11.These 8 values go in a stem-and-leaf diagram, the tens digit as the stem: 34, 21, 27, 50, 42, 51, 51, 38. Stem 2's row has 3 leaves.
True or false?
Answer:
12.Here are 8 players' heights in cm: 146, 144, 176, 144, 152, 163, 165, 166. 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:

13.May is drawing the table as a histogram (the left column is scores, the right players). Along the axis, the bars run from to in all.
Fill in each blank
Working:
Answer:
14.Chi-keung draws these data as a stem-and-leaf diagram, the tens digit as the stem: 78, 29, 72, 45, 68, 24, 33, 70. The stem of its last row is 8.
True or false?
Working:
Answer:
15.Chi-keung draws these 10 values as a stem-and-leaf diagram, the tens digit as the stem: 38, 30, 40, 54, 52, 67, 63, 57, 34, 49. Stem 4's row has leaves, the largest of them .
Fill in each blank
Working:
Answer:
16.Chi-keung is drawing scores grouped as 20–29, … as a histogram. Which way of doing it is right?
- A. Each bar runs from lower to upper boundary, the bars touching
- B. Leave a small gap between the bars
- C. Make each bar's width its class's frequency
- D. Start the vertical scale at the least frequency
Choose the right answer
Working:
Answer:
17.May draws 76, 63, 49, 65, 61 as a stem-and-leaf diagram, each row's leaves in order. What is the 3rd leaf in stem 6's row?
Working:
Answer:
18.Ka-yan weighs 8 players in kg: 54, 30, 30, 43, 30, 68, 38, 69. Which stem-and-leaf diagram shows them correctly?
- A
- B
- C
- D
Choose the right picture
Working:
Answer:

Show the answers and working

Drawing stem-and-leaf diagrams and histograms worksheet: Answers and working

1. 6
Least 14, greatest 69: stems 1 to 6, writing those with no data too, 6 − 1 + 1 = 6 stems.
2. 3, 4, 7
Stem 3's data are 37, 34, 33, with leaves 7, 4, 3; in order: 3, 4, 7.
3. 49.5, 59.5, 2
The bar runs from the lower boundary 49.5 to the upper 59.5, as tall as the frequency 2.
4. 4
A bar's height is its class's frequency: count the values from 30 to 39, 4 of them.
5. 39.5, 44.5, 1
The classes are 5 wide: 40–44 has boundaries 39.5 and 44.5, so the bar runs from 39.5 to 44.5. Count the values from 40 to 44: 1, the bar's height.
6. 34
First check the number of leaves: the diagram has only 7, but there are 8 values. Find each value in the diagram in turn; the one not there is 34.

7. A
Each value's tens digit is its stem and its units digit its leaf: 8 values, 8 leaves, each row in order.
8. A
Each value's tens digit is its stem and its units digit its leaf: 8 values, 8 leaves, each row in order.
9. False
Count the values with tens digit 3: 2, so stem 3's row has 2 leaves.
10. C. 29.5、39.5
The class 30–39 has boundaries 29.5 and 39.5: the bar runs from one to the other and touches the next.
11. False
Count the values with tens digit 2: 2, so stem 2's row has 2 leaves.
12. C
152 has stem 15 and leaf 2. 8 values make 8 leaves, each beside its stem, each row in order.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 19.5, 69.5
The first class's lower boundary is 20 − 0.5 = 19.5, the last class's upper boundary 69.5; the bars touch, with no gaps between. Their heights are the frequencies 6, 7, 5, 8, 12.
14. False
The last row is the greatest value's stem: the greatest is 78, stem 7.
15. 2, 9
2 values have tens digit 4; the largest of their units digits is 9, last in the row.
16. A. Each bar runs from lower to upper boundary, the bars touching
A histogram marks boundaries on its axis: the bar for 20–29 runs from 20 − 0.5 to 29 + 0.5, touching the next; heights are frequencies, from 0.
17. 5
Stem 6's leaves are 3, 5, 1; in order 1, 3, 5; the 3rd is 5.
18. C
Tens digit the stem, units the leaf; 8 values make 8 leaves, each row in order.

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