For problems 11 through 14 use the following exam scores. 83, 68, 84, 85, 75. 11. Find the mean if each score is weighted equally. 12. Find the mean if the first four exams are each weighted 10% and the fifth exam is weighted 60%. 13. Find the range and interquartile range. n Σ-3). 14. Find the variance. Hint: S i-1 n -1 15. Prove that when exam scores are weighted equally, the weighted mean is the same as the n Σ. n i= mean. i.e. Prove that when scores are weighted equally x,w n i-1 16. Prove that the sum of the deviations from the mean is always zero. i.e. Prove that(x-x) = 0. i-1 17. According to Chebyshev's Theorem what proportion of data is within (a) 1 standard deviation of the mean. (b) 1.5 standard deviations of the mean. (d) 2.5 standard deviations of the mean. dard deviations of the ean.

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Mr. Imperfecto teaches another math class.  This time he has 23 students take a test, the average score on which is an 87.  Mr. Imperfecto realizes he put the wrong grade in for a student.  He entered a 35, and the score should have been an 85.  To the nearest integer, what is the new class average?

2. If 4 times a number is added to 5, the result is 35 more than the number. Find the number.