Question
The following data set is the age of customers at the ice cream shop: \[ 18,52,42,36,5,31,29,22 \] Find the median.
Ask by Johnson Zimmerman. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The median age is 30.
Solution
1. **Order the data from least to greatest:**
The ordered data set is:
\[
5,\, 18,\, 22,\, 29,\, 31,\, 36,\, 42,\, 52
\]
2. **Determine the number of observations:**
There are \(8\) data points.
3. **Identify the middle two values:**
Since the number of observations is even, the median is the average of the \(\frac{n}{2}\)-th and the \(\left(\frac{n}{2}+1\right)\)-th terms.
- The \(4\)-th term is \(29\).
- The \(5\)-th term is \(31\).
4. **Calculate the median:**
\[
\text{Median} = \frac{29 + 31}{2} = \frac{60}{2} = 30
\]
The median is \(30\).
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Simplify this solution Beyond the Answer
To find the median, first, you need to sort the ages in ascending order: \[ 5, 18, 22, 29, 31, 36, 42, 52 \] Since there are 8 numbers (an even count), the median will be the average of the two middle values. The middle values are 29 and 31. So, the median is: \[ \frac{29 + 31}{2} = \frac{60}{2} = 30 \] Thus, the median age of customers at the ice cream shop is 30.
