Dot Plot Statistics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
A dot plot shows ages of participants in a fun run: 20(3 dots), 25(5 dots), 30(8 dots), 35(6 dots), 40(4 dots), 45(2 dots), 50(1 dot). Describe the shape of the distribution and estimate the median age.

Solution

  1. 1
    Step 1: Total participants: 3+5+8+6+4+2+1=293+5+8+6+4+2+1 = 29. The median is the 29+12=15\frac{29+1}{2} = 15th value when ordered.
  2. 2
    Step 2: Cumulative counts: 20→3, 25→8, 30→16. The 15th value falls in the 30 group. The distribution is roughly symmetric with a slight right skew (tail extends toward higher ages).

Answer

The distribution is roughly symmetric with a slight right skew, peaking at age 30. The median age is 30.
Reading a dot plot to find the median requires cumulative counting to locate the middle value. The shape of a distribution (symmetric, left-skewed, or right-skewed) is determined by where the longer tail extends relative to the peak.

About Dot Plot

A dot plot is a statistical chart that displays the frequency of data values using dots stacked above a number line. Each dot represents one observation, making it easy to see clusters, gaps, and the overall shape of a distribution for small to medium datasets.

Learn more about Dot Plot →

More Dot Plot Examples

Example 1 easy

The number of books students read last month: 0, 1, 2, 1, 3, 2, 1, 0, 2, 1, 4, 2. Create a dot plot

Example 2 medium

Two dot plots show test scores for Class A (scores clustered tightly around 75) and Class B (scores

Example 3 medium

Create a dot plot for the data: 3, 5, 5, 6, 6, 6, 7, 8. What is the mode?

Example 5 hard

A dot plot shows the number of absences for 20 students: 0(6), 1(5), 2(4), 3(2), 4(1), 8(1), 10(1).

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