# 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 weighted60%.13. Find the range and interquartile range.nΣ-3).14. Find the variance. Hint: Si-1n -115. Prove that when exam scores are weighted equally, the weighted mean is the same as thenΣ.ni=mean. i.e. Prove that when scores are weighted equally x,wni-116. Prove that the sum of the deviations from the mean is always zero.i.e. Prove that(x-x) = 0.i-117. 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 theean.

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I need help with number 15. help_outlineImage TranscriptioncloseFor 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. fullscreen
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Step 1

Mean and weighted mean:

Consider the items x1, x2, …, xn with weights w1, w2, …, wn. The formula for mean and weighted mean is as follows:

Step 2
1. Proof:

It is given that exam scores are weighted equally likely. Assume that there are n exam scores. Therefore, each exam scores ha...

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