The test scores of five students are 70, 80, 85, 90, and 95. If each score is increased by 5 points, what is the variance of the new scores?
Show the answer and explanation
Correct answer
A. 74
Principle or equation
Adding a constant to every data value does not change the variance. The variance is the average of the squared deviations from the mean.
Why this answer is correct
Original scores: 70,80,85,90,95. Mean = (70+80+85+90+95)/5 = 84. Deviations: -14,-4,1,6,11. Squares: 196,16,1,36,121. Sum = 370. Variance = 370/5 = 74. Adding 5 to each score shifts the mean to 89 but deviations remain the same, so variance remains 74.
Example
For data 2,4,6, variance is 8/3. Adding 10 gives 12,14,16, variance still 8/3.
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