Averages & Interpreting Data — Year 9 Practice Questions
Work through these Year 9 practice questions on averages and interpreting data. Try each one before revealing the worked solution.
Questions
Find the mean of 4, 6, 8, 10, 12.
Find the median of 3, 7, 9, 12, 15.
Find the mode of 2, 3, 3, 5, 7, 3, 8.
Find the range of 5, 8, 2, 11, 7.
A frequency table shows the value 2 (frequency 3), 3 (frequency 5) and 4 (frequency 2). Find the mean.
In a frequency table, the value 5 has the highest frequency. What is the mode?
Estimate the mean of grouped data: class 0–10 (midpoint 5, frequency 4) and class 10–20 (midpoint 15, frequency 6).
Class A has mean 60 and range 20; Class B has mean 60 and range 8. Which class is more consistent?
Answers & Worked Solutions
Question 1 Solution
Step 1: Total = 4 + 6 + 8 + 10 + 12 = 40.
Step 2: 40 ÷ 5 = 8.
Answer: 8
Question 2 Solution
Step 1: The data is already in order.
Step 2: The middle value is 9.
Answer: 9
Question 3 Solution
Step 1: 3 appears most often.
Step 2: So the mode is 3.
Answer: 3
Question 4 Solution
Step 1: Largest = 11, smallest = 2.
Step 2: 11 − 2 = 9.
Answer: 9
Question 5 Solution
Step 1: Σfx = 2×3 + 3×5 + 4×2 = 6 + 15 + 8 = 29.
Step 2: Σf = 3 + 5 + 2 = 10; mean = 29 ÷ 10 = 2.9.
Answer: 2.9
Question 6 Solution
Step 1: The mode is the value with the highest frequency.
Step 2: That value is 5.
Answer: 5
Question 7 Solution
Step 1: Σ(midpoint × f) = 5×4 + 15×6 = 20 + 90 = 110.
Step 2: Σf = 4 + 6 = 10; estimated mean = 110 ÷ 10 = 11.
Answer: 11
Question 8 Solution
Step 1: Both have the same mean, so compare the range.
Step 2: Class B has the smaller range (8), so it is more consistent.
Answer: Class B
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