Question

The number of people leaving a hotel each morning was recorded over a period of time. These data are summarised in the stem-and-leaf diagram below. Determine the mode and the median of the data Stem Leaf Frequency 2 7 9 9 3 3 5 4 5 2 2 3 4 6 01 4 8 9 2 3 3 6 6 6 8 01 4 5 5 7 6 4 7 2 3 2 8 1 1 A. mode = 54; median = 56 B. mode = 56; median = 52 C. mode = 27; median = 54 D. mode = 7; median = 52 Activate Windows

Answer 1

C. mode = 3-3; median = 46

Explanation:

Looking at the stem-and-leaf diagram, we can see that the stem values range from 2 to 8, and the leaf values range from 0 to 9. Let's arrange the data in ascending order:

11, 12, 12, 12, 13, 23, 23, 23, 24, 25, 25, 27, 27, 29, 33, 33, 33, 34, 34, 35, 45, 45, 46, 46, 46, 47, 54, 55, 55, 56, 56, 56, 57, 68, 68, 68, 69, 89, 89, 99

Now, let's determine the mode. From the stem-and-leaf diagram, we can see that the stem 2 has a frequency of 4, the stem 3 has a frequency of 9, the stem 4 has a frequency of 6, the stem 5 has a frequency of 5, the stem 6 has a frequency of 7, the stem 7 has a frequency of 4, and the stem 8 has a frequency of 2. Therefore, the mode is the stem-and-leaf combination with the highest frequency, which is 3-3.

To find the median, we need to locate the middle value in the data set. Since we have 39 data points, the median will be the value at the 20th position when the data is arranged in ascending order. Looking at our arranged data, the 20th value is 46. Therefore, the median is 46.

In conclusion, the mode of the data is 3-3 and the median is 46. Therefore, the correct answer is:

C. mode = 3-3; median = 46