Topic Review — Measures of Centre

Review Questions

1. Calculate all four measures: Fluency

   For each dataset, find the mean, median, mode, and range.

   1. {6, 9, 4, 8, 3, 9, 7}
   2. {20, 25, 22, 28, 25, 30, 18, 22}
   3. {11, 11, 13, 15, 17, 19, 11}
   4. {50, 55, 60, 65, 70, 75, 80}
   5. {4, 4, 4, 4, 4}

2. Find missing values: Fluency

   1. The mean of {8, 12, x, 10} is 11. Find x.
   2. The mean of 5 numbers is 14. Four of the numbers are 10, 16, 13, 18. Find the fifth number.
   3. The mean of {n, 5, 9, 7, 4} is 7. Find n.
   4. A dataset has a median of 10 and the values in order are: 6, 8, ?, 12, 15. What is the missing value?

3. Read from a stem-and-leaf plot: Fluency

   Use this stem-and-leaf plot showing distances (km) run in a month:

   Stem	Leaves
   1	5   8
   2	0   3   3   7
   3	1   4   4   9
   4	2   5

   Key: 2 | 3 = 23 km

   1. List all values.
   2. Find the mean, median, mode, and range.
   3. What does the median tell you about the typical distance run?

4. Choose the right measure: Understanding

   1. The prices of houses in a suburb are: $350k, $380k, $390k, $420k, $440k, $2.1M. Which measure of centre best describes the typical price? Explain.
   2. A baker records the number of croissants sold each day: 18, 20, 19, 21, 20, 22, 20. Which measure is most useful for ordering stock? Why?
   3. The range of test scores in one class is 5. The range in another class is 42. What does this tell you about each class?
   4. Can the mean ever equal the median? Give an example where this occurs.

5. Outliers and context: Understanding

   1. Dataset: {14, 16, 15, 17, 13, 16, 62}. Identify the outlier. Calculate the mean and median both with and without the outlier.
   2. Which measure changed more when the outlier was removed — the mean or the median? Explain why.
   3. True or False: removing an outlier always improves the accuracy of the mean. Explain.

6. Interpret and compare: Problem Solving

   Two swimmers track their times (seconds) for 50 m freestyle over 8 races:

   Swimmer A: 34, 36, 33, 37, 35, 34, 36, 35

   Swimmer B: 28, 40, 31, 43, 29, 42, 30, 41

   1. Find the mean, median, and range for each swimmer.
   2. Both swimmers have similar means. What does this tell you about their overall performance?
   3. Which swimmer is more consistent? Use the range to justify.
   4. A coach needs to select one swimmer for a race where consistency is critical. Who should be selected and why?
   5. Write a short paragraph (3–4 sentences) comparing the two swimmers, using at least three measures in your answer.

7. Quick calculations: Fluency

   1. Find the median of: 3, 7, 8, 12, 15, 21
   2. Find the median of: 5, 9, 11, 14
   3. Find the mode of: blue, red, red, green, blue, red, yellow
   4. The range of a dataset is 18. The smallest value is 9. What is the largest value?

8. Test scores for a class of 8 students: 72, 85, 91, 68, 85, 77, 93, 85. Understanding

   1. Find the mean, median, mode, and range.
   2. A ninth student joins and scores 100. How does this change the mean and median?
   3. Which measure best represents a “typical” score for the original 8 students? Explain.

9. A student’s assessment results were: 80, 75, 90, 85, x. The mean of all five results is 83. Understanding

   1. Find the value of x.
   2. What is the median of all five results?
   3. Is the mean a fair representation of the student’s performance? Explain.

10. Comparing two sports teams’ points per game: Problem Solving

    Team X: {12, 15, 14, 13, 16, 14, 12, 14}

    Team Y: {8, 20, 11, 18, 9, 22, 10, 18}

    1. Calculate the mean and range for each team.
    2. Which team scores more consistently? How do you know?
    3. Both teams play in a final. Which team would you back to win, and why? Justify using statistics.