Dot Plot Statistics Example 5

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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). Calculate the mean, identify any potential outliers, and explain how the outliers affect the mean compared to the median.

Solution

  1. 1
    Step 1: Mean = (0×6)+(1×5)+(2×4)+(3×2)+(4×1)+(8×1)+(10×1)20=0+5+8+6+4+8+1020=4120=2.05\frac{(0 \times 6)+(1 \times 5)+(2 \times 4)+(3 \times 2)+(4 \times 1)+(8 \times 1)+(10 \times 1)}{20} = \frac{0+5+8+6+4+8+10}{20} = \frac{41}{20} = 2.05.
  2. 2
    Step 2: The values 8 and 10 appear separated from the main cluster (0–4) by a gap — these are potential outliers. The median is the average of the 10th and 11th values: both are 1, so median = 1. The outliers pull the mean (2.05) above the median (1), demonstrating that the mean is sensitive to extreme values.

Answer

Mean = 2.05, Median = 1. Values 8 and 10 are outliers that pull the mean above the median. The median better represents the typical student's absences.
Outliers visible as isolated dots on a dot plot pull the mean toward them but leave the median relatively unchanged. When outliers are present, the median is often a better measure of centre because it resists the influence of extreme values.

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 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),

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