Math  /  Data & Statistics

QuestionEach of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100 . \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{ Sample of Size 5 data set } \\ \hline 108 & 119 & 95 & 92 & 93 & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{ Sample of Size 12} \\ \hline 108 & 119 & 95 & 92 & 93 & 96 \\ \hline 93 & 98 & 106 & 112 & 112 & 103 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{7}{|c|}{ Sample of Size 30 } \\ \hline 108 & 119 & 95 & 92 & 93 & 96 \\ \hline 93 & 98 & 106 & 112 & 112 & 103 \\ \hline 100 & 102 & 105 & 109 & 91 & 94 \\ \hline 98 & 98 & 112 & 104 & 100 & 91 \\ \hline 101 & 100 & 95 & 95 & 101 & 109 \\ \hline \end{tabular}
What is the median of the new sample of size 30 ? 100.5 (Type an integer or decimal rounded to one decimal place as needed.)
For each sample size, state what happens to the mean and median.
For each sample size, the mean remains constant, and the median substantially increases
Comment on the role that the number of observations plays in resistance. A. As the sample size increases, the impact of the misrecorded data on the mean decreases. B. As the sample size increases, the impact of the misrecorded data on the mean remains the same.

Studdy Solution
Comment on the role that the number of observations plays in resistance.
As the sample size increases, the impact of the misrecorded data on the mean decreases due to the averaging effect over a larger number of observations. The median is more resistant to changes in data because it depends on the middle value(s) and is less affected by outliers.
Answer: A. As the sample size increases, the impact of the misrecorded data on the mean decreases.\text{Answer: A. As the sample size increases, the impact of the misrecorded data on the mean decreases.}

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