A focused Grade 6 learning session for Mean and Median using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving mean and median.
Mean and Median means choosing a model, naming what each number means, and explaining the strategy.
Question: A dot plot shows the number of goals scored by 9 players: What is the median number of goals?
Why it works: Data: \(1, 2, 2, 3, 3, 3, 4, 4, 5\). The median (middle of 9 values) is the 5th value: \(3\).
Answer: \(3\)
Question: The stem-and-leaf plot shows test scores. What is the median?
| Stem | Leaf |
|---|---|
| 6 | 5, 7 |
| 7 | 2, 4, 8 |
| 8 | 1, 9 |
Answer: \(74\)
Question: The histogram shows the frequency distribution of test scores. Which range has the highest frequency?
Answer: Range 2
Question: A student's quiz scores are \(78, 82, 85, 88\). If the student gets a \(95\) on the next quiz, what is the new mean?
Why it works: New mean \(=\frac{78+82+85+88+95}{5}=\frac{428}{5}=85.6\).
Answer: \(85.6\)
Mean and Median becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Find the mean of the data set: \(4, 6, 8, 10, 12\).
Answer B: \(8\)
Mean \(=\frac{4+6+8+10+12}{5}=\frac{40}{5}=8\).
What is the mean of the numbers \(2, 4, 6, 8, 10\)?
Answer B: \(6\)
Mean \(=\frac{2+4+6+8+10}{5}=\frac{30}{5}=6\).
Find the mean of \(5, 15, 20, 30\).
Answer D: \(17.5\)
Mean \(=\frac{5+15+20+30}{4}=\frac{70}{4}=17.5\).
What is the median of the data set: \(3, 7, 9, 12, 15\)?
Answer A: \(9\)
The data is already ordered. The median is the middle value: \(9\).
Find the median of \(2, 5, 8, 11, 14, 17\).
Answer A: \(9.5\)
Median is the average of the two middle values (positions 3 and 4): \(\frac{8+11}{2}=9.5\).
The mean of \(5, 8, 12, x\) is \(10\). What is the value of \(x\)?
Answer A: \(15\)
Mean \(= \frac{5+8+12+x}{4}=10 \Rightarrow 5+8+12+x=40 \Rightarrow x=15\).
The data set is: \(2, 4, 6, 8, 30\). Which statement is true?
Answer C: Mean is greater than Median
Mean \(=\frac{2+4+6+8+30}{5}=10\). Median \(=6\) (middle value). Since \(10>6\), the mean is greater than the median. The outlier \(30\) pulls the mean up.
A science class recorded temperatures: \(18, 20, 22, 24, 26, 28\). What is the median?
Answer B: \(23\)
With 6 values, median is the average of the 3rd and 4th values: \(\frac{22+24}{2}=23\).
A dot plot shows the number of goals scored by 9 players: What is the median number of goals?
Answer B: \(3\)
Data: \(1, 2, 2, 3, 3, 3, 4, 4, 5\). The median (middle of 9 values) is the 5th value: \(3\).
The table shows quiz scores for 5 students. What is the mean score?
Answer C: \(88\)
Mean \(=\frac{85+90+88+92+85}{5}=\frac{440}{5}=88\).
Which data set would have the largest mean?
Answer D: \(1, 2, 3, 4, 50\)
Set D has a large outlier (\(50\)) that increases the mean to \(\frac{60}{5}=12\). The other sets have means of \(3\), \(5\), and \(4\) respectively.
