A focused Grade 6 learning session for Summarizing Data and Making Comparisons using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving summarizing data and making comparisons.
Summarizing Data and Making Comparisons means reading, creating, and explaining displays so data can answer real questions.
Question: Two classes recorded the time (in seconds) each student spent on a warm-up. Summary statistics: Which class had more consistent times?
| Class | Mean | Median | Range | IQR |
|---|---|---|---|---|
| Class A | 45 | 42 | 30 | 12 |
| Class B | 48 | 50 | 25 | 8 |
Why it works: Class B has a smaller range (\(25 < 30\)) and smaller IQR (\(8 < 12\)), indicating less spread and more consistent times.
Answer: Class B
Question: Two runners' sprint times (seconds) over 8 races. Which runner has more consistent sprint times?
Answer: Runner B
Question: Two manufacturing plants' defect rates (per 1000 units) are summarized below. Which plant's performance is more predictable?
| Plant | Mean | Median | Range |
|---|---|---|---|
| Plant X | 12 | 11 | 8 |
| Plant Y | 10 | 10 | 20 |
Answer: Plant X, because it has a lower range
Question: A dot plot shows the number of books read by 10 students: \(2, 3, 3, 4, 4, 4, 5, 5, 6, 6\). What is the median number of books?
Why it works: With 10 data points, the median is the average of the 5th and 6th values when ordered: \((4+5) \div 2 = 4.5\).
Answer: \(4.5\)
Summarizing Data and Making Comparisons becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Read the scale before reading the answer.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Class A scored a mean of \(82\) on a test; Class B scored a mean of \(76\) on the same test. Which statement is best supported by the data?
Answer B: Class A's typical score was higher than Class B's.
The mean represents a typical score. A higher mean in Class A (\(82>76\)) supports that Class A's typical score was higher, but not that every individual outperformed.
A dot plot shows the number of books read by 10 students: \(2, 3, 3, 4, 4, 4, 5, 5, 6, 6\). What is the median number of books?
Answer D: \(4.5\)
With 10 data points, the median is the average of the 5th and 6th values when ordered: \((4+5) \div 2 = 4.5\).
A dataset has a mean of \(50\) and a median of \(48\). Which statement is most likely true?
Answer B: There are some large values pulling the mean higher than the median.
When the mean exceeds the median, high outliers are typically present, skewing the distribution right.
A histogram shows test scores for a class. The data has a center (mean) of \(75\) and a spread (range) of \(30\). If the highest score is \(95\), what is the lowest score?
Answer C: \(65\)
Range = highest \(-\) lowest. \(30 = 95 - \text{lowest}\), so lowest \(= 95 - 30 = 65\).
Two classes recorded the time (in seconds) each student spent on a warm-up. Summary statistics: Which class had more consistent times?
Answer B: Class B
Class B has a smaller range (\(25 < 30\)) and smaller IQR (\(8 < 12\)), indicating less spread and more consistent times.
A box plot for Dataset X shows Q1 = \(20\), median = \(25\), Q3 = \(35\). A box plot for Dataset Y shows Q1 = \(22\), median = \(26\), Q3 = \(32\). Which statement is true?
Answer A: Dataset X has a larger interquartile range.
IQR for X \(= 35 - 20 = 15\); IQR for Y \(= 32 - 22 = 10\). Dataset X is larger.
A dot plot shows scores: \(\{3, 5, 7, 7, 8, 8, 8, 9\}\). What is the mode?
Answer D: \(8\)
The mode is the value appearing most frequently. The value \(8\) appears 3 times, more than any other value.
A dataset has 11 values arranged in order. The median is \(55\). If you remove the largest and smallest values, what will be the new median of the remaining 9 values?
Answer D: Cannot be determined without knowing all values.
The new median depends on the actual distribution. Removing extremes does not guarantee the new 5th value is still \(55\).
A histogram shows weights of 20 students. The shape is roughly symmetric. Which summary best describes the center?
Answer A: The mean, because symmetric data has mean \(\approx\) median.
For symmetric distributions, mean and median are nearly equal and both represent the center well.
Two basketball teams' season statistics: Which team had more consistent scoring?
Answer A: Hawks (lower standard deviation)
Standard deviation measures spread. Hawks' lower standard deviation (\(8 < 14\)) indicates more consistent scoring around their mean.
A dataset contains: \(10, 12, 14, 18, 20, 22\). What is the interquartile range (IQR)?
Answer B: \(8\)
The data is already ordered. With 6 values, the lower half is \(\{10, 12, 14\}\) giving \(Q_1 = 12\), and the upper half is \(\{18, 20, 22\}\) giving \(Q_3 = 20\). So \(\text{IQR} = Q_3 - Q_1 = 20 - 12 = 8\).
