The scores of 10 students in a test are 75, 80, 85, 90, 95, 100, 70, 80, 85. Find the median score.
The Correct Answer and Explanation is:
Correct Answer: Median = 82.5
Step-by-Step Explanation:
To find the median, you need to follow a clear, systematic process. The median is the middle value in a data set when the numbers are arranged in ascending order. If the number of values is odd, the median is the middle number. If the number is even, the median is the average of the two middle numbers.
Step 1: Arrange the scores in ascending order.
Given scores:
75, 80, 85, 90, 95, 100, 70, 80, 85
There are 9 scores listed here, but the problem says “10 students.” So we’re missing one number.
Let’s count:
Given: 75, 80, 85, 90, 95, 100, 70, 80, 85 → That’s 9 numbers, not 10.
Let’s assume the correct list includes all 10 values. Let’s add another value (maybe a typo excluded one). If a 90 is missing (a reasonable guess), here’s a corrected list of 10 values:
Correct list (assumed):
70, 75, 80, 80, 85, 85, 90, 90, 95, 100
Step 2: Find the middle numbers.
Since there are 10 values, the median will be the average of the 5th and 6th values.
Let’s identify those:
- 70
- 75
- 80
- 80
- 85 ← 5th
- 85 ← 6th
- 90
- 90
- 95
- 100
Step 3: Calculate the median.
Median=85+852=1702=85\text{Median} = \frac{85 + 85}{2} = \frac{170}{2} = 85
Final Answer: Median = 85
So, assuming there are 10 values, and using logical correction of missing data, the median score is 85. The median is a useful measure of central tendency because it is not affected by extreme scores, making it more representative in skewed data.
