Use this data set to answer the following question: 5, 10, 12, 4, 6, 11, 13, 5. Remember to show your work.
Calculate the median.
The Correct Answer and Explanation is :
To find the median of the data set (5, 10, 12, 4, 6, 11, 13, 5), follow these steps:
Step 1: Sort the Data
First, arrange the numbers in ascending order:
[
[4, 5, 5, 6, 10, 11, 12, 13]
]
Step 2: Determine the Number of Values
Next, count how many values are in the sorted list. In this case, there are 8 values (an even number).
Step 3: Calculate the Median
For a data set with an even number of observations, the median is calculated by taking the average of the two middle numbers. Here, the two middle numbers in the sorted list are the 4th and 5th values:
- 4th value: (6)
- 5th value: (10)
Now, calculate the median using the formula:
[
\text{Median} = \frac{\text{4th value} + \text{5th value}}{2} = \frac{6 + 10}{2} = \frac{16}{2} = 8.0
]
Conclusion
The median of the dataset (5, 10, 12, 4, 6, 11, 13, 5) is 8.0.
Explanation of the Median
The median is a measure of central tendency that provides a central value of a dataset. It is particularly useful because it is not influenced by outliers or extreme values. In this case, calculating the median involved sorting the values and then determining the average of the two middle values due to the even count of data points.
This characteristic of the median makes it a robust statistic in fields such as healthcare and finance, where it can provide a better representation of a typical value compared to the mean, especially in skewed distributions. In summary, the median offers a valuable insight into the central point of a dataset while minimizing the influence of anomalies.