What Are Measures of Central Tendency?
When we collect data, we often want a single value that best represents the whole dataset , a "typical" value. This is what measures of central tendency give us.
There are three main measures you need to know for IB Math AI SL:
Mean: The mean is the arithmetic average of a dataset, calculated by dividing the sum of all values by the number of values.
Median: The median is the middle value of a dataset when the values are arranged in ascending order. If there is an even number of values, it is the average of the two middle values.
Mode: The mode is the value that occurs most frequently in a dataset. A dataset can have one mode, more than one mode (bimodal, trimodal, etc.), or no mode at all.
Each measure has strengths and weaknesses depending on the shape of the data and whether outliers are present , choosing the right one matters!
Imagine your class's test scores. The mean gives a sense of overall performance, the median tells you what a "middle" student scored, and the mode tells you the most common score achieved. Each tells a slightly different story about the same data.
Calculating the Mean
The mean is the most commonly used measure of central tendency. The formula is straightforward:
where means "the sum of all data values" and is the total number of values.
Find the mean of the dataset: 4, 7, 9, 10, 12.
Step 1: Sum all the values:
Step 2: Count the number of values:
Step 3: Divide:
The mean is 8.4.
The mean is sensitive to outliers (extreme values). A single very large or very small value can pull the mean significantly away from most of the data. Always check your dataset for outliers before deciding whether the mean is the best measure to use.
On your GDC (graphical display calculator), you can enter a list of data and compute the mean instantly using the statistics functions. Practice doing this , it saves time in exams and reduces arithmetic errors.