Pregunta
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The median age is 30.
Solución
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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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.

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