### 21.3. Numerical Description of Data

We saw in Sec. 21–2 how we can describe a set of data by frequency distribution, a frequency histogram, a frequency polygon, or a cumulative frequency distribution. We can also describe a set of data with just a few numbers, and this more compact description is more convenient for some purposes. For example, if, in a report, you wanted to describe the heights of a group of students and did not want to give the entire frequency distribution, you might simply say:

The mean height is 58 inches, with a standard deviation of 3.5 inches.

The mean is a number that shows the center of the data; the standard deviation is a measure of the spread of the data. As mentioned earlier, a number such as the mean or the standard deviation may be found either for an entire population (and are thus population parameters) or for a sample drawn from that population (and so are sample statistics).

Therefore to describe a population or a sample, we need numbers that give both the center of the data and the spread. Further, for sample statistics, we need to give the uncertainty of each figure. This will enable us to make inferences about the larger population.

## Example 15:

A student recorded the running times for a sample of participants in a race. From that sample she inferred (by methods we'll learn later) that for the entire population of racers The mean time is ...

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