Analyzing Population Data
To describe a data set you report a center and a spread. Mean and median give the center; standard deviation measures how spread out the values are.
The mean is the balance point — add the values and divide by how many. It is the most common summary and the base for standard deviation.
Measures of center
The mean is the sum of the values divided by the count. The median is the middle value when the data is sorted.
The mean uses every value, so outliers pull it; the median resists them. Reporting both gives a fuller picture.
Measuring spread
Standard deviation measures the typical distance of values from the mean. A small standard deviation means the data clusters tightly; a large one means it is spread out.
Two data sets can share a mean but have very different spreads, which is why the spread number matters.
Worked examples
Example 1: computing the mean
Find the mean of .
Answer:
Example 2: mean vs median
Which measure of center is more affected by an outlier?
Answer: The mean
Example 3: finding the median
Find the median of .
Answer:
Try one yourself
Common questions
How do I find the mean?
Add all the values and divide by how many there are.
What does standard deviation tell me?
How far, on average, the values sit from the mean — the spread of the data. Small means tightly clustered; large means spread out.
When is the median better than the mean?
When outliers are present. The median ignores extreme values, so it better represents a skewed data set's center.
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