Final answer:
To assess the mean and median from a stem-and-leaf plot, add up all the values for the mean and locate the middle number(s) for the median. Outliers can be spotted if they lie far from the bulk of data. The distribution shape informs whether the mean and median will be close or skewed.
Step-by-step explanation:
To determine the mean and median from a stem-and-leaf plot, one must first understand the structure of the plot. Each number in the dataset is split into a stem (usually the leading digit(s)) and a leaf (the last significant digit). For example, in the number 23, the stem is 2 and the leaf is 3. To find the mean, add up all the numbers represented in the stem-and-leaf plot and divide by the count of the numbers. For the median, identify the middle number(s) in the ordered list of data points represented by the plot. Looking at the example provided: The data are distances (in kilometers) from a home to local supermarkets. A stemplot is created with leaves to the right of the decimal point. Once you've arranged the leaves in ascending order next to their corresponding stems, locate the center of the dataset by counting the total number of data points. If the count is odd, the median is the middle number. If it's even, the median is the average of the two central numbers.
For the given example with grades on a chemistry exam, we would list the stems, such as 7 for 70's, 8 for 80's, etc. Then add the leaves, which represent the units. After this, we can visually inspect for any potential outliers, which stand far away from the bulk of the data. When assessing the distribution of the data from the stem-and-leaf plot, consider the pattern of the leaves. If the leaves are symmetrically distributed around the middle stem, the mean and median would be close. However, if the plot is skewed, with more leaves on one side of the plot, this can indicate that the mean might be pulled in the direction of the skew, while the median remains centered. This is because the mean is affected by every value in the dataset while the median is only the middle value.