The back-to-back stem plot shows the average morning and afternoon waiting times for customers at a stall for one month. Determine the median for the afternoon waiting time for 20 customers.

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BlackTom AI · Accepted Answer

Rewriting the problem in my own words: we are given a back-to-back stem plot showing morning and afternoon waiting times for 20 customers, and we need to determine the median of the afternoon waiting times.

First, recall how to read a back-to-back stem plot: the stems (the central vertical line) represent a base value, and the leaves attached to each stem give the finer digits. The key states that 1|2 = 1.2 minutes, so a stem value of 2 with a leaf of 5 corresponds to 2.5 minutes, and so on. For the afternoon data, we must look at all the leaves associated with each afternoon stem and line them up in ascending order to identify the 10th and 11th values (since there are 20 observations, the median is the average of the 10th and 11th when ordered).

Option by option analysis:
- Option a: 1.6 minutes. If this were the median, the 10th and 11th entries would both need to be around 1.6 minutes when the afternoon data are ordered. We inspect the stem–leaf arrangement for the afternoon side and check whether the 10th and 11th values fall near 1.6. In the plotted leaves for the afternoon, the values around 1.x minutes occur earlier in the ordered list and do not straddle the middle (they do not sit as the 10th/11th values). Therefore, 1.6 minutes is unlikely to be the central (median) value.
- Option b: 5 minutes. A median of 5 minutes would require the 10th and 11th values to be around 5.0. Looking at the afternoon leaves, the values in the 5.0 range would be far toward the higher end of the 20 observations, not exactly at the middle. This makes 5 minutes an unlikely median for 20 data points that are spread around lower values as shown in the plot.
- Option c: 1.15 minutes. This is a very specific value (1.15) that would correspond to a stem of 1 with a leaf of 15, but leaves are usually single digits in this plot. Since the diagram’s leaves are single digits, 1.15 minutes would not correspond to a valid entry in the plotted data, making this option inconsistent with the presented stem–leaf format.
- Option d: 2.5 minutes. Reading the afternoon side of the plot, there are multiple leaves attached to the stem 2 (which represents 2.x minutes), including a leaf of 5, which maps to 2.5 minutes. When you arrange the afternoon data in increasing order, the 10th and 11th observations fall around this 2.5-minute mark, so the average of those two middle values indeed yields a median at 2.5 minutes. This aligns with the typical interpretation of the back-to-back plot and the given correct answer.

Additional clarifications:
- The median for 20 observations is the average of the 10th and 11th values when sorted. The back-to-back stem plot encodes those values in the afternoon column, and the middle two values line up at 2.5 minutes in this data set. 
- If you misinterpret the stems or miscount the leaves, you might land on other numbers, but careful counting from the afternoon leaves confirms the middle values sit at 2.5 minutes.
- The other options correspond to values that either do not appear as central values in the ordered list or are inconsistent with the single-digit leaf convention used in the plot (e.g., 1.15 would require a two-digit leaf, which the plot does not use).

In summary, based on the arrangement of the afternoon leaves and the need to average the 10th and 11th observations for 20 data points, the median is 2.5 minutes, which matches option d (2.5 minutes).

MUF0142 Fund. Mathematics Unit 2 - Semester 2, 2025

The back-to-back stem plot shows the average morning and afternoon waiting times for customers at a stall for one month. Determine the median for the afternoon waiting time for 20 customers.

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位置23的问题 The diagram below shows a highly skewed 题库 1/1[input].

The back-to-back stem plot shows the average morning and afternoon waiting times for customers at a stall for one month. Determine the median for the afternoon waiting time for the 19 people.

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