The back-to-back stem-and-leaf plot below shows the ages of patients seen by two doctors in a family clinic one day. Compare the ages of the patients of Doctor 1 and Doctor 2 using the mean and median of each data set.
Ages of doctor's patients
Doctor 1 Doctor 2
| 3 | 5
920 | 2 | 00236
875 | 1 | 37
973211 | 0 | 2239
I'm really confused on what im supposed to do
To compare the ages of the patients of Doctor 1 and Doctor 2 using the mean and median, we first need to understand what the back-to-back stem-and-leaf plot represents.
A stem-and-leaf plot is a way to organize and display data where the data values are split into two parts: the stem (leading digits) and the leaf (trailing digits). In this case, the stem represents the tens digit of the ages and the leaf represents the ones digit.
Let's start by analyzing Doctor 1's data:
Doctor 1:
| 3 | 5
920 | 2 | 00236
875 | 1 | 37
973211 | 0 | 2239
The stems in Doctor 1's data range from 87 to 97. The corresponding leaves for each stem form the values of the patients' ages. For example, for the stem 92, we have leaves 0, 2, and 3. This means there are three patients whose age starts with 92 and ends with 0, 2, or 3.
To find the mean of the ages of Doctor 1's patients, we need to calculate the sum of all the ages and then divide it by the total number of patients. In this case, we can add up all the ages in Doctor 1's data and divide by the total number of entries.
Mean of Doctor 1 = (920 + 875 + 973211 + 920 + 875 + 920 + 920 + 9732 + 9732 + 1 + 9731 + 1 + 9732 + 9732 + 9732 + 0 + 1 + 0 + 2 + 0 + 2 + 3 + 6 + 9) / 23
We get the sum of the ages by adding up all the numbers on the right side of the stem-and-leaf plot. Then we divide it by 23, which is the total number of entries.
Now, let's find the median of Doctor 1's ages. The median represents the middle value when the data is arranged in ascending order. Since we have 23 entries in Doctor 1's data, we can start by listing all the ages in ascending order and finding the middle value.
Sorted list of Doctor 1's ages: 0, 0, 1, 1, 2, 2, 3, 6, 9, 20, 23, 37, 875, 875, 920, 920, 920, 920, 9731, 9732, 9732, 9732, 9732, 973211
The median is the middle value of this sorted list, which in this case is 920.
Now, repeat the same process for Doctor 2's data and compare the mean and median of Doctor 2's ages with Doctor 1's ages to determine the comparison between the two doctors.
To compare the ages of the patients of Doctor 1 and Doctor 2 using the mean and median of each data set, follow these steps:
1. Understand the stem-and-leaf plot:
- The left column represents the stem (tens place) of the ages.
- The right column represents the leaf (ones and units place) of the ages.
- For Doctor 1, the stems are 9, 8, and 7, with corresponding leaves.
- For Doctor 2, the stems are 5, 2, 0, and 3, with corresponding leaves.
2. Calculate the mean (average) for each doctor:
- For Doctor 1: Add up all the ages of Doctor 1's patients and divide by the total number of patients in Doctor 1's dataset.
- For Doctor 2: Add up all the ages of Doctor 2's patients and divide by the total number of patients in Doctor 2's dataset.
3. Calculate the median for each doctor:
- For Doctor 1: Determine the middle value of Doctor 1's dataset (the age that divides it into two equal parts). If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.
- For Doctor 2: Determine the middle value of Doctor 2's dataset (the age that divides it into two equal parts). If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.
4. Compare the mean and median of each doctor's data set.
It's important to note that since the stem-and-leaf plot you provided doesn't specify the exact ages for each leaf, we won't be able to provide the exact mean and median values. However, you can follow the steps above to calculate them once you have the complete dataset.