Measure of central tendency
Compute mean, median, and mode as measures of central tendency in Grade 10 statistics, and choose the most appropriate measure for skewed or symmetric data sets.
Key Concepts
A measure used to represent the middle of a data set. The mean is the average ($\bar{x} = \frac{x 1 + x 2 + ... + x n}{n}$), the median is the middle number when the data is in order, and the mode is the number that appears most frequently.
For the grades {10, 12, 12, 13, 15, 16, 20}, find the measures of central tendency. Mean: $\bar{x} = \frac{10+12+12+13+15+16+20}{7} = \frac{98}{7} = 14$ Median: The middle value in the ordered list is 13. Mode: The value 12 appears most often, so it is the mode.
These three 'M's' are detectives trying to find the 'typical' value in a data set. The mean is the mathematical average, like splitting a pizza evenly among friends. The median is the true middle man when everyone lines up by size. The mode is simply the most popular kid in the class—the value that shows up most often.
Common Questions
How do you calculate mean, median, and mode?
Mean: sum all values divided by count. Median: middle value when sorted (average of two middle values for even count). Mode: most frequently occurring value.
When should you use median instead of mean?
Use median when data is skewed or contains outliers. For example, income data with extreme high values makes the mean misleadingly high; median better represents the typical value.
Can a data set have more than one mode?
Yes. A data set with two modes is bimodal; three or more modes is multimodal. If all values appear with equal frequency, the data has no mode.