Question

a teacher surveys 25 students to determine how many pens are in their backpacks. the teacher wants to display the data in a graph that allows the students to find both the median and the mean of the data. which type of graph would be best? a dot plot, because it shows all of the data points, so the mean and the median can both be found a scatter plot, because the trend of the data indicates which value, the mean or the median, is greater a histogram, because the median is in the middle interval and the mean is in the interval that contains the most data a box plot, because the median is represented on the plot and the mean can be calculated using the highest and lowest values

Explanation:

• Analyze each option:
• Dot plot: Shows all data points. To find the mean, we can sum all data points (visible on dot plot) and divide by the number of points (25). To find the median, we can order the data points (visible) and find the middle value (for 25 data points, the 13th value).
• Scatter plot: Used for showing relationships between two variables, not for displaying a single - variable data set to find mean and median.
• Histogram: Groups data into intervals. We don't know the exact data points, so we can't accurately calculate the mean (needs exact values) and the description of finding the median and mean is incorrect.
• Box plot: Shows median, quartiles, and extreme values, but not all data points. We can't calculate the mean accurately as we don't have all the data points (only know min, max, median, and quartiles).

Answer:

a dot plot, because it shows all of the data points, so the mean and the median can both be found