The Mean — Solutions

1. Calculate the Mean

   1. {3, 7, 5, 9, 1}: 5 ▶ View Solution
   2. {12, 15, 8, 14, 11}: 12 ▶ View Solution
   3. {6, 4, 8, 2, 10, 6}: 6 ▶ View Solution
   4. {23, 17, 31, 29, 20}: 24 ▶ View Solution
   5. {5.2, 3.8, 6.4, 4.6}: 5.0 ▶ View Solution
   6. {102, 98, 105, 107, 88}: 100 ▶ View Solution
   7. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}: 5.5 ▶ View Solution
   8. {14, 16, 18, 20, 22}: 18 ▶ View Solution

2. Effects on the Mean & Missing Values

   1. Adding 14 to {6, 8, 10, 12}: 10 ▶ View Solution
   2. Removing 8 from {6, 8, 10, 12}: ≈9.33 ▶ View Solution
   3. Missing 4th number (mean = 15): 16 ▶ View Solution
   4. Missing 6th number (mean = 20): 22 ▶ View Solution
   5. 4th test score needed for mean of 75: 80 ▶ View Solution
   6. Mean when each value increases by 5: 35 ▶ View Solution
   7. x = 10 ▶ View Solution
   8. n = 10 ▶ View Solution

3. When is the Mean Misleading?

   1. {5, 6, 6, 7, 7, 8, 55} mean misleading: Yes — outlier 55 pulls mean to 12.9; typical value is 6–7 ▶ View Solution
   2. Outlier in {31, 28, 33, 29, 35, 27, 98}: 98; mean with outlier = 40.1, without = 30.5 ▶ View Solution
   3. Real estate mean misleading: Yes — $4 800 000 outlier pulls mean to $1 332 000; four of five properties under $500 000 ▶ View Solution
   4. True or False — mean is always best: False — outliers can pull mean from centre; median is often better ▶ View Solution

4. Mean in Context

   1. Class scores + new student: 72 ▶ View Solution
   2. Rainfall & target: 65 mm ▶ View Solution
   3. Basketball 6th game: 25 points ▶ View Solution
   4. x = 2.4 kg ▶ View Solution

5. Complete the Calculation

   1. {9, 15, 12, 6, 18}: 12 ▶ View Solution
   2. {40, 50, 60}: 50 ▶ View Solution
   3. {7, 7, 7, 7, 7, 7}: 7 ▶ View Solution
   4. {100, 200, 300, 400}: 250 ▶ View Solution

6. Calculate from a Data Table

   1. Total: 75 ▶ View Solution
   2. Mean: 15 ▶ View Solution
   3. Above/below mean: Above: Bella, Diana  |  Below: Alex, Carlos, Ethan ▶ View Solution

7. True or False?

   1. Mean of {10, 10, 10, 10} is 10: True ▶ View Solution
   2. Adding a value equal to the mean doesn’t change the mean: True ▶ View Solution
   3. Mean must be one of the dataset values: False — e.g. {1, 2} has mean = 1.5 ▶ View Solution
   4. Doubling all values doubles the mean: True ▶ View Solution
   5. Mean of {1, 2, 3, 4, 100} > 20: True — mean = 22 ▶ View Solution
   6. Removing the largest value always decreases the mean: True ▶ View Solution

8. Spot the Error

   1. Error: Divided by 4 instead of 5 — {6, 9, 3, 12, 10} has 5 values ▶ View Solution
   2. Correct working: Sum = 40, Count = 5, Mean = 8 ▶ View Solution
   3. Why count carefully: Wrong count gives wrong mean even if sum is correct ▶ View Solution

9. Which is Correct?

   1. Which student: Student A — counted all 6 values ▶ View Solution
   2. Student B’s mistake: Counted 5 instead of 6 — forgot to include 9 ▶ View Solution
   3. Correct mean: 44 ÷ 6 ≈ 7.33 ▶ View Solution

10. Extended Investigation

    1. Mean of first 8 games: 3 goals per game ▶ View Solution
    2. After game 9 (0 goals): ≈2.67 goals per game ▶ View Solution
    3. Goals needed in game 10 to restore mean of 3: 6 ▶ View Solution
    4. Is “3 goals per game” accurate?: Yes — for games 1–8 only; after game 9 it drops to 2.67 ▶ View Solution