Final answer:
The best way to display a set of data with a narrow range for analyzing the central tendency and distribution shape is by using a box plot, as it effectively highlights the median, quartiles, and extremes without distortion.
Step-by-step explanation:
Best Ways to Display Data with a Narrow Range
To effectively display a set of data with a narrow range and to understand the measures of central tendency and the shape of the data, a box plot is often the best choice. A box plot provides a clear visualization of the data's central tendencies, including the median and the quartiles, allowing for easy comparison between different data sets. Furthermore, it offers a good graphical image of the concentration of the data and how far the extreme values are from most of the data. To construct a box plot, you would need to identify five key data points: the minimum value, the first quartile, the median, the third quartile, and the maximum value. These points help compare how close other data values are to them and are particularly useful for data sets with outliers or when the range of the data is not very wide.
While there are other methods to display data, such as histograms or pie charts, a box plot is advantageous for data with a narrow range as it emphasizes the measures of central tendency and the distribution's shape without being distorted by the data's limited variability.