Question 1: Find the mean of the following data set: 12, 15, 14, 16, 13.

Answer: 14

Question 2: Calculate the mean of the data represented by this stem and leaf diagram: Stem | Leaves 1 | 2, 4, 5 2 | 1, 3, 5 3 | 0, 2, 4

Answer: 22

Question 3: A class of 30 students took a test. The scores (out of 100) are as follows: 65, 70, 72, 75, 80, 85, 90, 95, 100. Find the mean score.

Answer: 78.2

Question 4: Construct a stem and leaf diagram for the following data: 22, 24, 27, 29, 31, 33, 36, 38.

Answer: See student drawing on grid.

Question 5: A factory produces items with weights (in grams): 50, 52, 55, 58, 60, 62, 65. Find the mean weight.

Answer: 57

Question 6: Using data from a stem and leaf diagram, students recorded their test scores: 68, 70, 72, 75, 78, 80. Find the mean score.

Answer: 73.8

Question 7: A basketball team scored points in 10 games as follows: 80, 85, 78, 90, 88, 85, 92, 77, 84, 86. Calculate the average (mean) score.

Answer: 84.5

Question 8: A survey recorded the ages of participants: 15, 16, 16, 17, 18, 19, 20, 21. Find the mean age.

Answer: 17.25

Question 9: A group of 12 students completed a quiz. Their scores are: 45, 50, 55, 55, 60, 65, 70, 75, 80, 85, 90, 95. Find the mean score.

Answer: 71.25

Question 10: Explain why calculating the mean is useful when analyzing data from a stem and leaf diagram.

Answer: It helps to find the average value, giving a quick summary of the data's central tendency.

Question 11: A common mistake is to add all data points without dividing by the number of points. Identify and correct this error in calculating the mean.

Answer: They forgot to divide the total sum by the number of data points.

Question 12: Challenge: The data set is large: 100, 102, 105, 110, 115, 120, 125, 130, 135, 140. Find the mean and explain how the mean would change if the highest value (140) was replaced with 150.

Answer: Mean = 118; replacing 140 with 150 increases the mean to 119.75, showing the average increases.