Pre-Algebra
Data and graphs
Mean, median, mode
20 practice questions
0 video lessons
Theory + worked examples
Mean, Median, Mode
California Pre-Algebra • Standard 6.SP.5 • Data & Graphs
Mean, Median, Mode is a topic in Data & Graphs in the California Common Core State Standards. It is aligned to Standard 6.SP.5, which requires students to find and interpret the mean, median, and mode of a data set.
Mean, median, and mode measure the center of a data set: the average, the middle value, and the most frequent value.
Theory
Measures of center summarize a data set:
- Mean: the sum divided by the count.
- Median: the middle value when ordered.
- Mode: the most frequent value.
Order the data before finding the median.
Center of a small data set.
The three measures.
The mean:
\[\bar x=\dfrac{\text{sum of values}}{\text{number of values}}\]
The median is the middle of the ordered list.
How to find each measure
- Mean: add all values, divide by the count.
- Median: order the data, take the middle.
- For an even count, average the two middle values.
- Mode: find the most frequent value.
Example 1 — Mean
Find the mean of \(2,4,4,5,10\).
Solution
Add and divide by \(5\).
| \(\dfrac{25}{5}\) | \(=\) | \(5\) |
Example 2 — Median
Find the median of \(2,4,4,5,10\).
Solution
Middle value in order.
| \(\text{median}\) | \(=\) | \(4\) |
Example 3 — Mode
Find the mode of \(2,4,4,5,10\).
Solution
Most frequent.
| \(\text{mode}\) | \(=\) | \(4\) |
Example 4 — Even count
Find the median of \(3,5,7,9\).
Solution
Average the two middle values.
| \(\dfrac{5+7}{2}\) | \(=\) | \(6\) |
Common pitfalls
Order the data first for the median.
An even count averages the two middle values.
There can be no mode or several.
Frequently asked questions
What is the mean?
The average — sum divided by count.
What is the median?
The middle value when ordered.
What is the mode?
The most frequent value.
Median of \(3,5,7,9\)?
\(6\).
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