Find the median of the scores 75, 21, 56, 36, 81,05, 42
The Correct Answer and Explanation is:
Let’s first correctly interpret the data and find the median step by step.
Step 1: List the scores
The scores are:
75, 21, 56, 36, 81, 05, 42
Note: “05” is just another way of writing 5 (a single-digit score with a leading zero).
So, the corrected list is:
75, 21, 56, 36, 81, 5, 42
Step 2: Arrange the numbers in ascending order
Order the scores from least to greatest:
5, 21, 36, 42, 56, 75, 81
Step 3: Find the median
The median is the middle number in an ordered list.
There are 7 numbers in this list, which is odd, so the median is the 4th number.
Ordered list again: 5, 21, 36, 42, 56, 75, 81
👉 Median = 42
✅ Final Answer: 42
✍️ Explanation
The median is a measure of central tendency in statistics. It represents the middle value of a dataset when it is arranged in numerical order. Finding the median helps summarize the dataset by identifying the point where half of the values are lower and half are higher, which can provide a more accurate reflection of a “typical” value, especially in skewed data.
In this problem, the scores given are: 75, 21, 56, 36, 81, 05, 42. It’s important to recognize that “05” is simply the number 5, written with a leading zero. It doesn’t change the value but is often used in formatting. So, we rewrite the dataset as: 75, 21, 56, 36, 81, 5, 42.
Next, we arrange the scores in ascending order: 5, 21, 36, 42, 56, 75, 81. This step is crucial since the median depends entirely on the position of numbers within the ordered list, not the order in which they were originally given.
Since there are 7 values (an odd number), the median is the number in the middle position, which is the 4th value in the ordered list. Counting in, the fourth number is 42. Thus, the median score is 42.
The median is especially useful because it is not affected by extreme values or outliers. For instance, if the highest score was an outlier like 150, the average (mean) would shift, but the median would remain more stable. Therefore, the median gives a more reliable sense of the central value in datasets with irregular distributions.
In conclusion, the median of the scores is 42.
