Calculating Mean and MAD from Dot Plots
Calculating the Mean Absolute Deviation (MAD) from a dot plot requires first translating each dot back into a data value — every dot represents one value, even when stacked. Then follow three steps: find the mean, find each value distance from the mean, and average those distances. For a dot plot with values 2, 3, 3, 4: mean = 3, distances are 1, 0, 0, 1, MAD = 0.5. This skill from Reveal Math, Course 1, Module 10 connects visual data displays to numerical calculation in 6th grade statistics.
Key Concepts
You can calculate the MAD directly from visual graphs like dot plots. To do this accurately, you must first translate the visual dots back into a list of numbers. Remember that every single dot represents one data value, even if they are stacked on top of each other.
Common Questions
How do I find the MAD from a dot plot?
First, list every dot as a number value. Find the mean. Then find the absolute distance from each value to the mean. Finally, average those distances. That average is the MAD.
What does each dot on a dot plot represent?
Each dot represents exactly one data value. If two dots are stacked on top of the number 4, then 4 appears twice in the data set.
How many values do I divide by when finding the MAD from a dot plot?
Divide by the total number of dots on the plot. Each dot is one value, so if there are 10 dots, you divide the sum of distances by 10.
A dot plot shows values 2, 3, 3, 4. What is the MAD?
Mean = (2+3+3+4)/4 = 3. Distances: |2-3|=1, |3-3|=0, |3-3|=0, |4-3|=1. MAD = (1+0+0+1)/4 = 0.5.
What is a common mistake when calculating MAD from a dot plot?
Not counting stacked dots as separate values. If three dots are stacked on the number 5, you must include three separate 5s in your data list and divide by the full total.
When do 6th graders calculate MAD from dot plots?
Module 10 of Reveal Math, Course 1 covers this in the Statistical Measures and Displays unit.