Question

determine whether each statement makes sense or does not make sense, and explain your reasoning. im working with data sets with different means and the same standard deviation. choose the correct answer below. o a. the statement makes sense. the mean of a data set is completely unrelated to the standard deviation of a data set. thus data sets can have different means and the same standard deviation. o b. the statement does not make sense. data sets can never have the same standard deviation unless they are the same data set, in which case their means would be the same. o c. the statement makes sense. data sets can have different means and the same standard deviation. for example, if two data sets contained the values {1,3} and {2,4}, the means for each would be 2 and 3 respectively, but they both have the same standard deviation of approximately 1.41421. o d. the statement does not make sense. if data sets have different means, then they must have different standard deviations.

Explanation:

• Option A: The mean and standard deviation are related (e.g., standard deviation measures dispersion around the mean), so the statement is wrong.
• Option B: Data sets with different values can have the same standard deviation (e.g., {1,3} and {2,2} have different means but same standard deviation), so the statement is wrong.
• Option C: Data sets can have different means but the same standard deviation. For example, data set 1: {1,1} (mean = 1, standard deviation = 0) and data set 2: {2,2} (mean = 2, standard deviation = 0) or the given {1,1} and {2,2} (mean 1 vs 2, standard deviation ~1.4142 for both). So this statement makes sense.
• Option D: Different means don’t force different standard deviations (as shown in examples), so the statement is wrong.

Answer:

C. The statement makes sense. Data sets can have different means and the same standard deviation. For example, if two data sets contained the values {1,1} and {2,2} the means for each would be 2 and 3 respectively, but they both have the same standard deviation of approximately 1.41421.