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.

Question

BlackTom AI · Accepted Answer

First, identify that there are 19 afternoon waiting times, so the median corresponds to the 10th value when the data are arranged in increasing order.
Next, read the stem-and-leaf plot for the Afternoon column. The stems are the whole-number part, and the leaves are the tenths digits, with the value equal to stem + leaf/10. For the Afternoon data:
- Stem 0 has leaves: 7, 8, 8, which correspond to 0.7, 0.8, 0.8.
- Stem 1 has leaves: 1, 1, 2, 4, 4, 5, 6, 6, 7, which correspond to 1.1, 1.1, 1.2, 1.4, 1.4, 1.5, 1.6, 1.6, 1.7.
Count how many data points accumulate as we go:
- Up to Stem 0: 3 data points (0.7, 0.8, 0.8).
- Including Stem 1: add 9 more data points, bringing the total to 12 data points up to 1.7.
Since the 10th value lies within Stem 1 (between the 4th and 12th overall values, in order), we locate the 10th value specifically in the sequence of leaves for Stem 1: 1, 1, 2, 4, 4, 5, 6, 6, 7.
The 10th overall value is the (10 − 3) = 7th value within Stem 1’s leaves, which is the leaf 6, corresponding to 1.6 minutes.
Therefore, the median afternoon waiting time for the 19 people is 1.6 minutes.
Now, briefly consider the other options:
- 2.5 minutes would be a much higher value corresponding to later stems/leaves (far above the 10th position for 19 data points), so it cannot be the median here.
- 1.15 minutes would require a leaf of 5 under Stem 1 or a specific 1.15 entry, which is not present in the provided leaves for Stem 1 (the leaves are 1,1,2,4,4,5,6,6,7).
- 5 minutes would require a stem of 5, which is not represented in the Afternoon data here, so that value is not in the dataset.
Thus, among the given choices, 1.6 minutes aligns with the 10th value in the ordered Afternoon data as shown by the stem-and-leaf plot.

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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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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