Question
The stem-and-leaf plot shows the ages of a group of friends. Find the median age.
Stem-and-Leaf Plot of Friends Ages
Stem Leaf
2 8
3 1 2 4
4 2 7 9
5 4
Key: 2|8=28
years
(1 point)
years
Answers
GPT-4o mini
To find the median age from the stem-and-leaf plot, we first need to list all the ages represented in the plot.
From the stem-and-leaf plot, we have:
- Stem 2: Leaf 8 → 28
- Stem 3: Leaves 1, 2, 4 → 31, 32, 34
- Stem 4: Leaves 2, 7, 9 → 42, 47, 49
- Stem 5: Leaf 4 → 54
Now let's list all the ages in order:
- 28
- 31
- 32
- 34
- 42
- 47
- 49
- 54
Now we have the ages: 28, 31, 32, 34, 42, 47, 49, 54 (a total of 8 values).
To find the median of a data set with an even number of observations, we take the average of the two middle numbers. The middle numbers in this ordered list of 8 values are the 4th and 5th ages:
- 4th age: 34
- 5th age: 42
Now, we calculate the average of these two middle numbers:
\[
\text{Median} = \frac{34 + 42}{2} = \frac{76}{2} = 38
\]
Therefore, the median age is **38 years**.
From the stem-and-leaf plot, we have:
- Stem 2: Leaf 8 → 28
- Stem 3: Leaves 1, 2, 4 → 31, 32, 34
- Stem 4: Leaves 2, 7, 9 → 42, 47, 49
- Stem 5: Leaf 4 → 54
Now let's list all the ages in order:
- 28
- 31
- 32
- 34
- 42
- 47
- 49
- 54
Now we have the ages: 28, 31, 32, 34, 42, 47, 49, 54 (a total of 8 values).
To find the median of a data set with an even number of observations, we take the average of the two middle numbers. The middle numbers in this ordered list of 8 values are the 4th and 5th ages:
- 4th age: 34
- 5th age: 42
Now, we calculate the average of these two middle numbers:
\[
\text{Median} = \frac{34 + 42}{2} = \frac{76}{2} = 38
\]
Therefore, the median age is **38 years**.