A focused Grade 6 learning session for Describing Data: Center, Spread, and Shape using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving describing data: center, spread, and shape.
Describing Data: Center, Spread, and Shape means reading, creating, and explaining displays so data can answer real questions.
Question: The dot plot below shows the number of books read by students in one month. What is the median number of books read?
Why it works: Data: \(2, 2, 3, 3, 3, 4, 4, 5, 6, 6\) (10 values). Median is average of 5th and 6th values: \((3 + 3) / 2 = 3\).
Answer: 3
Question: Which dot plot shows data with a symmetric distribution?
Answer: Plot A (symmetric)
Question: Two classes compared their quiz scores using dot plots. Class X has dots clustered at 8--9. Class Y has dots spread from 3--10. What can you infer?
Answer: Class X has a smaller range (more consistent)
Question: Using the same dot plot from the previous question, what is the mean number of books read (rounded to the nearest whole number)?
Why it works: Sum = \(2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 + 6 + 6 = 38\). Mean = \(38 \div 10 = 3.8\), which rounds to 4.
Answer: 4
Describing Data: Center, Spread, and Shape 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.
Which of the following describes the CENTER of a data set?
Answer B: Median
Measures of center include the mean and median. Range, interquartile range, and maximum describe the spread or extremes of the data.
What is the mean of the data set: \(3, 5, 7, 9, 11\)?
Answer D: 7
Sum = \(3 + 5 + 7 + 9 + 11 = 35\). Mean = \(35 \div 5 = 7\).
Find the median of: \(2, 8, 4, 6, 10, 5, 3\).
Answer B: 5
Order the data: \(2, 3, 4, 5, 6, 8, 10\). The middle value is the 4th value, which is 5.
Which measure describes the SPREAD of a data set?
Answer C: Range
Spread measures include range, interquartile range (IQR), and mean absolute deviation (MAD). Mean and median are measures of center; mode is the most frequent value.
What is the range of the data set: \(12, 28, 5, 45, 19\)?
Answer C: 40
Range = Maximum \(-\) Minimum = \(45 - 5 = 40\).
What is the mode of: \(1, 2, 2, 3, 3, 3, 4\)?
Answer A: 3
The mode is the value that appears most often. The value 3 appears three times.
The dot plot below shows the number of books read by students in one month. What is the median number of books read?
Answer A: 3
Data: \(2, 2, 3, 3, 3, 4, 4, 5, 6, 6\) (10 values). Median is average of 5th and 6th values: \((3 + 3) / 2 = 3\).
Using the same dot plot from the previous question, what is the mean number of books read (rounded to the nearest whole number)?
Answer B: 4
Sum = \(2 + 2 + 3 + 3 + 3 + 4 + 4 + 5 + 6 + 6 = 38\). Mean = \(38 \div 10 = 3.8\), which rounds to 4.
A data set has a mean of 15 and a median of 12. What does this tell us about the shape of the data?
Answer D: The data is skewed right
When mean > median, the data is skewed right. The mean is pulled toward the larger outliers on the right.
The histogram shows the heights (in inches) of students in a class. Which interval contains the most students?
Answer B: 62--64 inches
The tallest bar in the histogram represents the 62--64 inch interval with 5 students.
Which dot plot shows data with a symmetric distribution?
Answer A: Plot A (symmetric)
Plot A forms a triangle shape with a peak in the middle (at 3), with equal tails on both sides. Plot B has outliers on the right, making it skewed right.
