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

1 answer

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

From the given stem-and-leaf plot:

  • The stem "2" with leaf "8" represents the age 28.
  • The stem "3" with leaves "1 2 4" represents the ages 31, 32, and 34.
  • The stem "4" with leaves "2 7 9" represents the ages 42, 47, and 49.
  • The stem "5" with leaf "4" represents the age 54.

Now, let's list all the ages:

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

Now we count the total number of ages: There are 8 ages.

To find the median:

  1. Since there is an even number of observations (8), the median will be the average of the 4th and 5th ages when the ages are sorted.
  2. The sorted list of ages is: 28, 31, 32, 34, 42, 47, 49, 54

The 4th and 5th ages are:

  • 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.