Learning Goal: A full summary reports the count, what was measured and its units, measures of center and spread, and what they mean in context.
Vocabulary
attributeThe thing being measured or counted in a data set (for example, number of books).
unitsThe measurement label, such as books, minutes, or centimeters.
countHow many data values (observations) were collected.
contextThe real-world situation the data comes from, which gives the numbers meaning.
What You Need to Know
A complete summary tells: (1) how many values, (2) what was measured and the units, (3) a measure of center, (4) a measure of variability, and (5) what it all means in context.
Choose the median and IQR when there are outliers or skew; choose the mean and MAD when data is fairly symmetric.
Always include the units so the numbers make sense (e.g., 'a typical student read 4 books').
Center answers 'What is typical?'; spread answers 'How much do values differ?'
Explain the measure in plain words tied to the situation, not just a number.
An outlier can make the mean misleading, so the median may better describe a typical value.
Worked Example I Do — watch how it works
Eight students recorded books read: 2,3,3,4,4,4,5,7. Summarize the data.
Step 1. Count and attribute: 8 students; the attribute is number of books read (units = books).
Step 2. Center: mean = 32 ÷ 8 = 4 books; median = (4+4)/2 = 4 books.
Step 3. Spread: range = 7 − 2 = 5 books. In context, a typical student read about 4 books.
Answer: 8 students; center = 4 books (mean and median); range = 5 books.
Guided Practice We Do — try it together
1. Data (ages in years): 11,12,12,12,13. State the count and the attribute with units.
💡 Hint: How many values, and what is being measured?
2. For 11,12,12,12,13, find the mean (center) in years.
💡 Hint: Sum is 60; divide by 5.
3. Data: 4,4,5,5,30 (minutes). Should you use mean or median to describe a typical value? Why?
💡 Hint: Is there an outlier?
Independent Practice You Do — show your work
1. Data (pets): 0,1,1,2,2,2,3. State the count and the units.
2. Data (minutes): 6,8,10,12,14. Find the mean and the units.
3. Data (points): 8,8,9,10,10,11. Find the median.
4. Data (hours): 2,3,3,4,4,4,5. Find the range and state its meaning.
5. Data (steps): 100,100,100,100,900. Which measure of center best describes a typical value, mean or median? Why?
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.SP.B.5.
Item 1Selected Response6.SP.B.5
A data set of test scores has one very low outlier. Which pair best describes a typical score and its spread?
Select the correct answer.
Item 2Selected Response6.SP.B.5
Data (books): 1,2,2,3,3,3,4,5. What is the median number of books?
Select the correct answer.
Item 3Constructed Response6.SP.B.5
Data (minutes of exercise): 10,10,15,20,25,30. Give the count, mean, and range with units.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
Count = 7 students; units = pets.
Independent 2
Mean = 10 minutes.
Independent 3
Median = (9+10)/2 = 9.5 points.
Independent 4
Range = 3 hours; values differ by 3 hours from least to most.
Independent 5
Median = 100 steps; the outlier 900 makes the mean misleading.
Item 1 · 6.SP.B.5
B — With an outlier, the median and IQR resist extremes and best describe center and spread.
Item 2 · 6.SP.B.5
C — With 8 values, the median is the average of the 4th and 5th values: (3+3)/2 = 3.
Item 3 · 6.SP.B.5
Count = 6; mean ≈ 18.3 minutes; range = 20 minutes. — Sum is 110 over 6 values for the mean; range is 30 − 10 = 20 minutes.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.SP.B.5