Fifteen candidates appeared in an examination. The marks of the candidates who passed in the examination are 9, 6, 7, 8, 8, 9, 6, 5, 4 and 7. What is the median of marks of all the fifteen candidates?
6
This problem requires us to find the median value of the marks obtained by all fifteen candidates in an examination. We are given the marks of only those candidates who passed.
The median represents the middle value in a dataset when the data points are arranged in ascending or descending order. If there is an odd number of data points (\(N\)), the median is the value at the middle position, which is calculated using the formula \(((N+1)/2)\). If there is an even number of data points (\(N\)), the median is the average of the two middle values located at positions \((N/2)\) and \(((N/2)+1)\).
To determine the median, the first step is to arrange the combined list of all 15 marks in ascending order:
We have a total of \(N = 15\) data points (marks). Since \(N\) is an odd number, the median is the single value located exactly in the middle of the sorted dataset.
Let's identify the 8th value from the sorted list:
0, 0, 0, 0, 0, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9
The 8th value in this ordered list is 6.
Based on the analysis and the assumption for the marks of the failed candidates, the median of the marks of all fifteen candidates is 6.
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