Mean, Median and Mode
In short: Mean, median and mode are three ways to name a typical value: the fair-share average, the middle entry once sorted, and the entry that shows up most often.
6th GradeStatistics6.SP.A.3
What is Mean, Median and Mode?
Mean, median and mode each answer the question “what is a typical value?” in a different way. They can disagree, so it helps to know what each one measures.
Share everything out equally and each person gets the mean. Line everyone up by size and the one standing in the middle shows the median, or the pair in the middle gets averaged when the line has an even count. The value met most often is the mode, and a list may have one, several or none.
How to spot it
- A question asks for the “average”, the “middle” or the “most common” value of a data set.
- Data are shared out evenly, as when equal totals are redistributed among everyone.
- A single very large or very small value makes you wonder which center is more reliable.
- A shop owner wants the best-selling size, which is a mode question.
The method
- Write the values in order from smallest to largest.
- For the mean, total everything and split by the count of entries.
- For the median, take the center entry, or the average of the two centers if the count is even.
- For the mode, look for the entry with the biggest tally, and watch for ties among the mean, median and mode work.
Mean, Median and Mode: solved example
Problem
A high school basketball player in Tulsa scored 14, 18, 18, 21, 25 and 30 points in six games. Find the mean, median and mode.
Solution
Mean: \(14 + 18 + 18 + 21 + 25 + 30 = 126\), and \(126 \div 6 = 21\).
Median: six values, so average the 3rd and 4th: \(\frac{18 + 21}{2} = 19.5\). Mode: 18 appears twice. The answers are mean 21, median 19.5, mode 18.
Try it
Question 1
Find the mean, median and mode of 7, 7, 9, 12, 15.
Show the answer
Sum 50, so mean 10. The middle value is 9. The most common value is 7.
Question 2
Four friends have a mean of 12 pieces of fruit. What is their total?
Show the answer
\(12 \cdot 4 = 48\) pieces.
Mean, Median and Mode vs. Range
Mean, median and mode describe the center of a data set, where it is typical. The range describes the spread, how far the data stretch from smallest to largest. Two data sets can share a center but have very different spreads.
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Whole dictionary: A–Z · 6th Grade · Statistics