100, 88, 76, 78, 92, 94, 84, 98, 82, 90 What is the Nicole’s median score?
The Correct Answer and Explanation is:
To find Nicole’s median score from the given set of scores (100, 88, 76, 78, 92, 94, 84, 98, 82, 90), we first need to arrange the scores in ascending order:
Step 1: Arrange the scores in ascending order.
- 76
- 78
- 82
- 84
- 88
- 90
- 92
- 94
- 98
- 100
Step 2: Identify the number of scores.
There are 10 scores in total, which is an even number. When calculating the median in a dataset with an even number of observations, the median is found by taking the average of the two middle numbers.
Step 3: Determine the two middle scores.
In this ordered list, the two middle scores are the 5th and 6th scores:
- 5th score: 88
- 6th score: 90
Step 4: Calculate the median.
To find the median, we average these two middle scores:
[
\text{Median} = \frac{88 + 90}{2} = \frac{178}{2} = 89
]
Therefore, Nicole’s median score is 89.
Explanation of the Median
The median is a measure of central tendency that indicates the middle point of a dataset. It is particularly useful because it is not affected by outliers or extreme values, providing a better representation of a typical score in a skewed dataset.
In this case, arranging the scores helps identify the central values effectively. The process of finding the median involves ensuring that the dataset is sorted, which allows for the identification of the middle scores. Since there is an even number of observations, the median is determined by averaging the two middle scores. This process is essential in statistics, especially when analyzing test scores, as it offers insight into overall performance without being skewed by particularly high or low scores.
In summary, the median score of Nicole’s test results is 89, highlighting her performance in a way that balances the influence of all scores within the dataset.