Table: Examination Marks (out of 100)

Candidate	Exam 1	Exam 2	Exam 3
Candidate X	82	78	85
Candidate Y	88	86	90

Which candidate achieved the greater mean score across all three examinations?

The correct option is Candidate Y.

To determine which candidate achieved the greater mean score across all three examinations, we need to calculate the mean (average) score for both Candidate X and Candidate Y.

Step 1: Calculate the mean score for Candidate X

Candidate X's scores in the three examinations are 82, 78, and 85.

First, find the sum of Candidate X's scores:

$\text{Sum for Candidate X}=82+78+85=245$

Now, divide the total sum by the number of examinations (3):

$\text{Mean for Candidate X}=\frac{245}{3}\approx 81.67$

Step 2: Calculate the mean score for Candidate Y

Candidate Y's scores in the three examinations are 88, 86, and 90.

First, find the sum of Candidate Y's scores:

$\text{Sum for Candidate Y}=88+86+90=264$

Now, divide the total sum by the number of examinations (3):

$\text{Mean for Candidate Y}=\frac{264}{3}=88$

Step 3: Compare the mean scores

Comparing the two mean scores:

Candidate X's mean score = 81.67

Candidate Y's mean score = 88

Since 88 > 81.67, Candidate Y achieved the greater mean score across all three examinations.