Question

Compute Median for the following data set

146 152 168 174 180 178 179 180 178 178 168 165 152 144

Hint:

Always cross out values as you arrange them to ensure you haven't missed any. If the count of sorted data doesn't match the original \( n \), you missed a value.

Answer 1

Step 1: Understanding the Concept:
The median is the middle value of a data set when the values are arranged in ascending or descending order.
Step 2: Key Formula or Approach:
For an even number of observations (\( n \)), the median is the average of the \( (\frac{n}{2})^{th} \) and \( (\frac{n}{2} + 1)^{th} \) terms.
Step 3: Detailed Explanation:
1. Count the data points: \( n = 14 \). Since 14 is even, we need the 7th and 8th terms.
2. Arrange in Ascending Order:
144, 146, 152, 152, 165, 168, 168, 174, 178, 178, 178, 179, 180, 180.
3. Identify the 7th and 8th terms:
7th term \( = 168 \)
8th term \( = 174 \)
4. Calculate Median: \[ \text{Median} = \frac{168 + 174}{2} = \frac{342}{2} = 171 \] Step 4: Final Answer:
The median of the data set is 171.