6th Grade Mean, Median, Spread and Box Plots Lesson (Free PDF)
This center spread lesson for 6th Grade covers mean, median, spread and box plots (Common Core 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d), with a free PDF to print.
The mean is the sum of the data divided by the number of values, the median is the middle value, and the mode is the most common value. Spread is measured by the range, the interquartile range (IQR), or the mean absolute deviation (MAD). A box plot shows the five-number summary. With outliers, use the median.
Grade 6 · Common Core State Standards: 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d
Key facts in this center spread lesson
- Mean = sum divided by the number of values; median = middle value.
- Range = greatest minus least; IQR = Q3 minus Q1.
- MAD is the average distance of the values from the mean.
- A box plot shows the minimum, Q1, median, Q3, and maximum.
- Outliers pull the mean but not the median.
What are the mean, median, and mode?
The mean is the sum of the values divided by how many there are. It is the equal share if everyone had the same amount. The median is the middle value of the ordered data, or the mean of the two middle values. The mode is the most common value.
For 4, 8, 6, 10, 12, the sum is 40, so the mean is \(40 \div 5 = 8\). The median is 8 as well.
How do you measure spread?
The range is the greatest value minus the least. The mean absolute deviation (MAD) is the average distance of the values from the mean. For 2, 4, 6, 8 the mean is 5, the distances are 3, 1, 1, 3, and the MAD is \(\frac{8}{4} = 2\).
What is a box plot?
For 2, 4, 5, 7, 8, 9, 12, 14, the median is 7.5, Q1 is 4.5, Q3 is 10.5, and the IQR is \(10.5 – 4.5 = 6\). The box holds the middle half of the data.
Which measures should you use?
- Draw a dot plot, histogram, or box plot first to see the shape.
- If the data are fairly symmetric, the mean and MAD describe it well.
- If the data are skewed or have outliers, use the median and the IQR.
- Always say what the numbers mean in the story.
Example: Salaries of 30, 32, 35, 36, 38, and 250 thousand dollars have a mean of about 70.2 but a median of 35.5. The outlier 250 pulls the mean up, so the median describes a typical salary better.
Center spread lesson: questions and answers
How do you find the mean?
Add all the values and divide by how many values there are. The mean of 4, 8, 6, 10, 12 is 40 divided by 5, which is 8.
How do you find the median when there is an even number of values?
Order the data and take the mean of the two middle values. For 2, 4, 6, 10 the median is (4 + 6) / 2 = 5.
What is the interquartile range?
The IQR is Q3 minus Q1. It shows how spread out the middle half of the data is.
What is the mean absolute deviation?
The MAD is the average of the distances of each value from the mean. For 2, 4, 6, 8, the mean is 5 and the MAD is 2.
When should you use the median instead of the mean?
Use the median when the data are skewed or have an outlier, because outliers pull the mean but barely change the median.
How to use this center spread lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the center spread lesson as a PDF with the button below and keep it with your notes.
All Grade 6 chapters: Grade 6 math.
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