The stem-and-leaf plot shows the ages of a group of friends. Find the median age.

Question

Stem | Leaf
2 8
3 1 2 4
4 2 7 9
5 4
Key: 2|8=28 years

__ years

Answer 1

To find the median age from the given stem-and-leaf plot, we first need to list out all the ages represented in the plot.

The ages from the stem-and-leaf plot are:

• Stem 2: Leaf 8 → 28
• Stem 3: Leaf 1 → 31
• Stem 3: Leaf 2 → 32
• Stem 3: Leaf 4 → 34
• Stem 4: Leaf 2 → 42
• Stem 4: Leaf 7 → 47
• Stem 4: Leaf 9 → 49
• Stem 5: Leaf 4 → 54

Now, let's list all the ages in order:

28, 31, 32, 34, 42, 47, 49, 54

Next, we count the total number of ages. There are 8 ages in total:

1. 28
2. 31
3. 32
4. 34
5. 42
6. 47
7. 49
8. 54

Since there are 8 data points (an even number), we find the median by averaging the two middle numbers. The two middle ages are the 4th and 5th numbers in the ordered list:

4th number: 34 5th number: 42

Now calculate the median:

\[ \text{Median} = \frac{34 + 42}{2} = \frac{76}{2} = 38 \]

Therefore, the median age is 38 years.