Dot Plots and Histograms

Learn dot plots, histograms, histogram bins.

Lesson 1 of 33 parts Practice Flashcards

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Dot Plots

Objective: Explain dot plots, apply the stated method, and check its conditions.

A dot plot places one mark per observation above its numerical value. Repeated values stack marks at the same location. It preserves individual value frequencies and is often suitable for small numerical datasets; count marks rather than distinct positions to recover sample size. Distinct value positions and total observations are different counts.

Formulas

Sample size = total dot count

Worked examples

Try itA synthetic dot plot shows 6 dots at value 7, 7 dots at value 8, and 1 dot at value 9. How many observations are shown?Show answer

Step 1: Each dot represents one observation. Step 2: Add the dot counts 6+7+1. Step 3: There are 14 observations; repeated values get stacked dots.

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Dot Plots

Objective: Explain dot plots, apply the stated method, and check its conditions.

Formulas

Sample size = total dot count

Worked examples

Try itA synthetic dot plot shows 6 dots at value 7, 7 dots at value 8, and 1 dot at value 9. How many observations are shown?Show answer

Step 1: Each dot represents one observation. Step 2: Add the dot counts 6+7+1. Step 3: There are 14 observations; repeated values get stacked dots.

Histograms

Objective: Explain histograms, apply the stated method, and check its conditions.

A histogram groups numerical observations into intervals and displays frequencies or densities. For equal-width frequency bins, bar heights are counts and total count is their sum. With unequal widths and density axes, bar area—not raw height—represents relative frequency. Unequal-width density histograms require reading areas.

Formulas

For equal-width count bins: n=Σfrequency

Worked examples

Try itA histogram has equal-width bin frequencies 42, 49, and 7. How many observations are represented?Show answer

Step 1: Each observation is counted in exactly one bin. Step 2: Add 42+49+7. Step 3: There are 98 observations.

Histogram Bins

Objective: Explain histogram bins, apply the stated method, and check its conditions.

A bin’s width is upper boundary minus lower boundary. A consistent half-open convention assigns boundary values to exactly one bin. Choices of bin width can reveal or hide shape; a histogram is an aggregation, not the complete raw dataset. Specify an endpoint convention to avoid duplicate counts.

Formulas

Width = upper boundary − lower boundary

Worked examples

Try itA histogram’s first bin runs from 7 inclusive to 13 exclusive. Find its width.Show answer

Step 1: Bin width is upper boundary minus lower boundary. Step 2: Compute (13)−7. Step 3: The width is 6; endpoint conventions prevent double counting.

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