Answer :
The mean of the new marks, after changing the original marks according to the linear equation y = 2x - 12, is 32. The mean of the new marks is 32. So, the correct answer is option c. 32.
The question states that there is a group of 13 students, and the mean (average) of their marks is 22. Each mark is then changed according to the linear equation y = 2x - 12. We need to find the mean of the new marks.
To find the new mean, we need to calculate the sum of the new marks and divide it by the number of students.
Let's find the sum of the new marks by substituting the original marks into the equation y = 2x - 12.
Original marks: x1, x2, x3, ..., x13
New marks: y1, y2, y3, ..., y13
Sum of new marks: (2x1 - 12) + (2x2 - 12) + (2x3 - 12) + ... + (2x13 - 12)
Using the distributive property, we can rewrite this as:
2(x1 + x2 + x3 + ... + x13) - 12 * 13
We know that the sum of the original marks is equal to the number of students multiplied by the mean:
Sum of original marks = 13 * 22 = 286
So the sum of the new marks becomes:
2 * 286 - 12 * 13
Now, we divide this sum by the number of students (13) to find the new mean:
(2 * 286 - 12 * 13) / 13
Simplifying the expression, we get:
(572 - 156) / 13
416 / 13
32
Therefore, the mean of the new marks is 32. So, the correct answer is option c. 32.
By substituting the original marks into the equation and finding the new sum, we can determine the new mean. This approach ensures accuracy and provides a step-by-step explanation.
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