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Learning Goal: Numerical data can be shown with dot plots, histograms, and box plots, each useful for seeing center, spread, and shape.

Vocabulary

dot plotA graph that shows each data value as a dot above a number line.
histogramA bar graph that shows how many values fall into equal intervals (bins); bars touch.
box plotA graph that shows the minimum, Q1, median, Q3, and maximum (the five-number summary).
frequencyHow many times a value or interval occurs in the data.
five-number summaryThe minimum, Q1, median, Q3, and maximum of a data set.

What You Need to Know

  • Dot plot: one dot per data value; tall stacks show the most common values. Best for small data sets.
  • Histogram: bars show how many values fall in each equal interval (bin); the bars touch and you read frequency.
  • Box plot: the box goes from Q1 to Q3, a line inside marks the median, and 'whiskers' reach the min and max.
  • In a box plot, the box length is the IQR and the whisker ends show the full range.
  • Dot plots and histograms show shape (peaks, gaps, skew); box plots show spread by quarters.
  • To make any display, first order the data and find the values you need (counts, bins, or the five-number summary).

Worked Example I Do — watch how it works

Data (minutes read): 10,12,15,15,18,20,22,25,25,28,30,35. Find the five-number summary for a box plot.
  1. Step 1. 12 values. Median = average of 6th and 7th values = (20+22)/2 = 21.
  2. Step 2. Lower half (first 6): 10,12,15,15,18,20 → Q1 = (15+15)/2 = 15.
  3. Step 3. Upper half (last 6): 22,25,25,28,30,35 → Q3 = (25+28)/2 = 26.5; min = 10, max = 35.
Answer: Min 10, Q1 15, Median 21, Q3 26.5, Max 35.

Guided Practice We Do — try it together

  1. 1. For a dot plot of 3,3,4,4,4,5, which value has the tallest stack?
    💡 Hint: Which value appears most often?
  2. 2. A histogram has bins 0–9, 10–19, 20–29. The value 14 goes in which bin?
    💡 Hint: Which interval contains 14?
  3. 3. Data: 2,4,6,8,10,12. Find the median for a box plot.
    💡 Hint: Six values: average the 3rd and 4th.

Independent Practice You Do — show your work

  1. 1. Data: 1,2,2,3,3,3,4. For a dot plot, how many dots go above the value 3?
  2. 2. Histogram bins 0–4, 5–9, 10–14. In which bin does the value 9 belong?
  3. 3. Data: 5,7,9,11,13. Find the median for a box plot.
  4. 4. Data: 4,6,8,10,12,14,16,18. Find Q1 and Q3 for a box plot.
  5. 5. Which display best shows each individual data value for a small set of 8 numbers — a dot plot or a histogram?

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.4.
Item 1Selected Response6.SP.B.4

Which display groups data into equal intervals and uses bars that touch?

Select the correct answer.

Item 2Selected Response6.SP.B.4

In a box plot, what does the line inside the box represent?

Select the correct answer.

Item 3Constructed Response6.SP.B.4

Data: 8,10,12,14,16,18. Give the five-number summary for a box plot.

Enter your answer in the space provided. Show your work.

Enter your answer:
Teacher Answer Key (click to show)
Independent 13 dots.
Independent 2The 5–9 bin.
Independent 3Median = 9 (the middle value).
Independent 4Median = 11; Q1 = 7, Q3 = 15.
Independent 5A dot plot, because it shows every single value as a dot.
Item 1 · 6.SP.B.4B — A histogram bins data into equal intervals with touching bars showing frequency.
Item 2 · 6.SP.B.4B — The line inside the box marks the median; the box edges are Q1 and Q3.
Item 3 · 6.SP.B.4Min 8, Q1 10, Median 13, Q3 16, Max 18. — Median = (12+14)/2 = 13; lower half gives Q1 = 10; upper half gives Q3 = 16.
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.SP.B.4