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)

1 answer

To find the median age from the stem-and-leaf plot, we first need to extract the ages from the plot.

From the plot:

  • 2 | 8 → 28
  • 3 | 1 2 4 → 31, 32, 34
  • 4 | 2 7 9 → 42, 47, 49
  • 5 | 4 → 54

Now, listing all the ages in order:

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

Now, we count the total number of data points. There are 8 ages in total.

To find the median, we:

  1. If the number of data points is odd, the median is the middle number.
  2. If the number of data points is even, the median is the average of the two middle numbers.

Since 8 is even, we take the average of the 4th and 5th values in the sorted list:

  • The 4th number is 34.
  • The 5th number is 42.

Now, we calculate the median:

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

Thus, the median age is 38.