To determine which data displays can be used to find the median of a given data set, we need to understand what a median is and how each type of display represents data.
1. Boxplot: A boxplot, also known as a box-and-whisker plot, shows the distribution of data based on a five-number summary (minimum, first quartile, median, third quartile, and maximum). It prominently displays the median as a line within the box, making it an ideal tool for identifying the median.
2. Dot Plot: A dot plot displays each data point as a dot along a number line. By arranging the data points in order, it is relatively simple to find the median by locating the middle value or the average of the two middle values if the total number of data points is even.
3. Histogram: A histogram groups data into bins or intervals and represents the frequency of data points within each interval using bars. While a histogram provides a visual representation of the distribution of the data, it does not explicitly display individual data values or their order. Therefore, it is less straightforward to pinpoint the median directly from a histogram without additional calculations or data points.
In this case, only the boxplot (I) and the dot plot (II) can be used straightforwardly to find the median of the ages of the yoga students. Hence, the histogram (III) is not ideal for this purpose.
Therefore, the correct answer is:
C. I only
