Example Card：Finding and Interpreting Mean, Median, Mode, and Range
Finding and Interpreting Mean, Median, Mode, and Range is a Grade 6-7 statistics skill where students calculate each measure of central tendency and spread from a data set. Students also learn to interpret what each value tells us about the data and when each measure is most useful.
Key Concepts
What happens when there’s a huge age gap in your club’s members? Example Problem: A music teacher lists the ages of her students: $$ 22 \quad 27 \quad 26 \quad 40 \quad 43 \\ 21 \quad 68 \quad 66 \quad 32 \quad 29 $$ Find the mean, median, mode, and range.
Step by Step: 1. Add all the ages to find the sum: $22 + 27 + 26 + 40 + 43 + 21 + 68 + 66 + 32 + 29 = 374$ 2. To find the mean, divide total by the number of students ($10$): $$ \operatorname{mean} = \frac{374}{10} = 37.4 $$ 3. Put the ages in order: $21, 22, 26, 27, 29, 32, 40, 43, 66, 68$ 4. Since there are $10$ ages, the median is the mean of the $5$th and $6$th numbers: $29$ and $32$ $$ \operatorname{median} = \frac{29 + 32}{2} = 30.5 $$ 5. There’s no repeated age, so there is no mode . 6. The range is the difference, highest minus lowest: $$ \operatorname{range} = 68 21 = 47 $$.
Takeaway: Big outliers (like two students much older than the rest) pull the mean up, but the median stays closer to most students’ ages. Sometimes, the median is a better measure of what’s typical!
Common Questions
How do you find the mean of a data set?
Add all the values and divide by the number of values. The mean is the average.
How do you find the median?
Arrange the values in order from least to greatest and find the middle value. If there is an even number of values, average the two middle values.
How do you find the mode?
The mode is the value that appears most often in a data set. There can be more than one mode or no mode.
What is the range of a data set?
The range is the difference between the maximum and minimum values: range = max minus min.
When is the median a better measure than the mean?
The median is better when data has outliers, since the mean is pulled toward extreme values but the median is not.