Question
The ages (in years) of 10 teachers in a school are \( 32,44,53,47,37,54,34,36,40,50 \). Find the median age.
Ask by Lyons Willis. in India
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The median age of the teachers is 42 years.
Solution
To find the **median** age of the 10 teachers, follow these steps:
1. **List the Ages:**
\[
32,\,44,\,53,\,47,\,37,\,54,\,34,\,36,\,40,\,50
\]
2. **Sort the Ages in Ascending Order:**
\[
32,\,34,\,36,\,37,\,40,\,44,\,47,\,50,\,53,\,54
\]
3. **Determine the Median:**
- Since there are **10** data points (an even number), the median is the average of the 5th and 6th values in the sorted list.
- **5th value:** 40
- **6th value:** 44
4. **Calculate the Median:**
\[
\text{Median} = \frac{40 + 44}{2} = \frac{84}{2} = 42
\]
**Therefore, the median age of the teachers is 42 years.**
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Simplify this solution Bonus Knowledge
To find the median age, first, we need to arrange the ages in ascending order: \( 32, 34, 36, 37, 40, 44, 47, 50, 53, 54 \). Since there are 10 ages (an even number), the median will be the average of the 5th and 6th values in this ordered list. The 5th age is 40 and the 6th age is 44. So, we calculate the median as follows: \[ \text{Median} = \frac{40 + 44}{2} = \frac{84}{2} = 42 \] Thus, the median age of the teachers is \( 42 \) years.
