Find the sample median in the data set 5,5,-10, 6, -3, -3
The correct answer and explanation is:
Correct Answer: -1
Explanation:
The median is the middle number in a sorted list of numbers. If the data set has an odd number of values, the median is the number exactly in the middle. If the data set has an even number of values, the median is the average of the two middle numbers.
Here is the step-by-step process:
Step 1: List the data
The given data set is:
5, 5, -10, 6, -3, -3
Step 2: Arrange the data in ascending order
-10, -3, -3, 5, 5, 6
Step 3: Count the number of data points
There are 6 numbers in the data set. Since 6 is even, we will use the formula: Median=3rd value+4th value2\text{Median} = \frac{\text{3rd value} + \text{4th value}}{2}
From the sorted list:
- 3rd value = -3
- 4th value = 5
Median=−3+52=22=1\text{Median} = \frac{-3 + 5}{2} = \frac{2}{2} = 1
However, this shows a contradiction from the earlier answer, so let’s double-check:
Sorted list: -10, -3, -3, 5, 5, 6
3rd value: -3
4th value: 5 Median=−3+52=22=1\text{Median} = \frac{-3 + 5}{2} = \frac{2}{2} = \boxed{1}
Final Answer: 1
Additional Explanation:
The median is not affected by extreme values like the mean is. For example, although -10 is quite far from the rest of the numbers, it does not pull the median down. Instead, the median only depends on the middle values, making it a more robust measure of central tendency, especially when the data contains outliers.
The reason we sort the numbers is to clearly see which values are in the middle. In this case, the third and fourth numbers after sorting give us the average needed to calculate the median.
So, after checking again, the correct median of the dataset 5, 5, -10, 6, -3, -3 is: 1\boxed{1}