\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline 43 & 52 & 35 & 27 & 26 & 51 & 48 & 36 \\
\hline 42 & 37 & 62 & 44 & 50 & 26 & 40 & 30 \\
\hline
\end{tabular}
...
Which data display(s) can be used to find the median for the ages of the yoga students?
1. box plot
II. dot plot
III. histogram
A. I, II, and III
B. II and III
C. I and II
D. I only
Understanding the Median
The median is a measure of central tendency that represents the middle value in a dataset when the data is arranged in order. To find the median, we need to arrange the data in ascending order and then identify the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
Data Displays and the Median
Let's analyze each data display option to see if it can be used to find the median:
Box Plot
A box plot, also known as a box-and-whisker plot, is a visual representation of data that summarizes five key statistics: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box plot visually represents the median as a line within the box, making it a suitable method to find the median.
Dot Plot
A dot plot uses dots to represent each data point along a number line. While a dot plot can help visualize the distribution of data, it doesn't explicitly display the median. To find the median from a dot plot, you would need to count the dots and manually determine the middle value.
Histogram
A histogram is a bar graph that shows the frequency distribution of data within specific intervals or ranges. It doesn't directly display the median. To find the median from a histogram, you would need to calculate the cumulative frequency and locate the interval that contains the median value.
The Correct Answer
Therefore, the correct answer is **C. I and II**. A box plot (I) directly displays the median, while a dot plot (II) can be used to find the median by manually counting and determining the middle value. A histogram (III) doesn't directly display the median.