Survey data are organized and interpreted by distinguishing categorical responses from numerical measurements and representing their frequencies or distributions with tables, dot plots, histograms, or box plots. Analysis compares groups and describes a distribution’s center using the mean or median, its spread using measures such as range or interquartile range, and its overall shape, while recognizing that an unrepresentative sample or misleading scale can distort conclusions; formal statistical inference and advanced measures are beyond this scope.
Survey data can be categorical or numerical:
For numerical data, organize the values and describe the center, spread, and shape of the distribution.
Example: A teacher surveys 10 students about how many minutes it takes them to get to school.
The responses are:
Step 1: Make a frequency table.
| Minutes | Frequency |
|---|---|
| 8 | 1 |
| 10 | 2 |
| 12 | 3 |
| 15 | 2 |
| 18 | 1 |
| 40 | 1 |
The data are numerical, so we can calculate a mean, median, and range.
Step 2: Find the mean.
Add all the values and divide by the number of students:
The mean travel time is 15.2 minutes.
Step 3: Find the median.
The values are already in order. There are 10 values, so use the middle two values, the fifth and sixth:
The median travel time is 12 minutes.
Step 4: Find the range.
Subtract the smallest value from the largest value:
The range is 32 minutes.
Step 5: Describe the distribution.
Most students take between 8 and 18 minutes, but one student takes 40 minutes. That unusual value stretches the data to the right, so the distribution is right-skewed. Because of this unusual value, the median of 12 minutes better describes a typical student than the mean of 15.2 minutes.
A clear conclusion is:
Most students take about 12 minutes to get to school. The times vary by 32 minutes, and one unusually large time makes the distribution right-skewed.
When making a conclusion from survey data, remember that the sample should represent the larger group. For example, surveying only students who live far from school might give a misleading picture of the travel times for the whole school.
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?