Question

Question

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

This stem-and-leaf plot represents the ages of a group of friends. The stem represents the tens place, and the leaves represent the ones place.
Stem Leaf
2 8
3 1 2 4
4 2 7 9
5 4
Key: 2|8=28 years

(1 point)
years

Answer 1

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

From the stem-and-leaf:

• 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 we can compile the ages in ascending order:

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

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

To find the median when the total number of observations (n) is even, we take the average of the two middle numbers.

The middle numbers are the 4th and 5th ages:

• 4th age: 34
• 5th age: 42

Now we calculate the median: \[ \text{Median} = \frac{34 + 42}{2} = \frac{76}{2} = 38 \]

Thus, the median age is 38 years.