Question 1: Explain why including the 'tens' digit in the Key is important when constructing a Stem and Leaf diagram.

Answer: It helps interpret the data correctly by showing the value of the tens digit, preventing confusion between numbers with similar units.

Question 2: Identify the mistake in the following Key: 'Stem: 3, Leaf: 1, 4, 7' for data 31, 34, 37.

Answer: The Leaf should include all units; if 37 is data, the leaf should be 7, but the mistake might be missing 37 or mislabeling.

Question 3: Construct a correct Key for the following data: 22, 25, 23, 26, 24.

Answer: Key: Stem: 2, Leaf: 2, 3, 4, 5, 6

Question 4: Why is it mistaken to use only the last digit of each number as the Leaf without considering the Stem?

Answer: Because it ignores the tens place, which is essential for accurate data grouping and interpretation.

Question 5: A student's Key shows 'Stem: 4, Leaf: 0, 5' but the data includes 40, 45, 44. What is the mistake?

Answer: They missed 44 in the Leaf; the correct Leaf should be 0, 4, 5.

Question 6: Given the data set: 31, 34, 32, 35, 33, identify a common error in the Key students might make and explain how to avoid it.

Answer: Students might forget to include all units in the Leaf or mislabel the Stem. To avoid this, double-check each data point and include all units.

Question 7: Construct a Stem and Leaf diagram for the data: 51, 52, 50, 55, 53. Then, write the correct Key.

Answer: Key: Stem: 5, Leaf: 0, 1, 2, 3, 5

Question 8: A student writes the Key as 'Stem: 10s, Leaf: 1s' for data 21, 22, 23. Why is this inaccurate and how can it be improved?

Answer: Because '10s' and '1s' are vague. It's better to specify 'Stem: 2, Leaf: 1, 2, 3' to clearly show the tens and units.

Question 9: Error analysis: A Key shows 'Stem: 7, Leaf: 4, 8' for data 74, 78. What's the mistake, and how can it be corrected?

Answer: The mistake is only including two leaves; it should include all units: 4 and 8. The corrected Leaf is 4, 8.

Question 10: Challenge Question: Given the data 91, 92, 93, 94, 95, construct the correct Stem and Leaf diagram with an appropriate Key. Then, explain any common pitfalls to avoid.

Answer: Key: Stem: 9, Leaf: 1, 2, 3, 4, 5. Common pitfalls include missing data points or mislabeling the Stem as 'tens' or 'units' incorrectly, which can lead to misinterpretation of the data.