Total blood cholesterol level was measured for each of 10 adults. Here are the 10 measurements (in $\mathrm{mg} / \mathrm{dL}$ ). \[ 224,194,238,148,172,149,140,209,220,151 \] Send data to calculator \begin{tabular}{|l|l|} \hline \begin{tabular}{l} (a) What is the median of this data set? If your answer is not \\ an integer, round your answer to one decimal place. \end{tabular} & \\ \hline \begin{tabular}{l} (b) What is the mean of this data set? If your answer is not an \\ integer, round your answer to one decimal place. \end{tabular} & \\ \hline \begin{tabular}{l} (c) How many modes does the data set have, and what are \\ their values? Indicate the number of modes by clicking in the \\ appropriate circle, and then indicate the value(s) of the \\ mode(s), if applicable. \end{tabular} & zero modes \\ \hline \end{tabular} $\times 5$
Solution
Step 1 ：First, arrange the data in ascending order: 140, 148, 149, 151, 172, 194, 209, 220, 224, 238
Step 2 ：Since there are 10 data points, the median is the average of the 5th and 6th data points. So, calculate the median using the formula \(\frac{172 + 194}{2}\)
Step 3 ：\(\boxed{183}\) is the median of this data set in mg/dL
Step 4 ：To find the mean of the data set, add up all the data points and divide by the number of data points. So, calculate the mean using the formula \(\frac{140 + 148 + 149 + 151 + 172 + 194 + 209 + 220 + 224 + 238}{10}\)
Step 5 ：\(\boxed{184.5}\) is the mean of this data set in mg/dL
Step 6 ：A mode is a value that appears most frequently in a data set. Looking at our data set, we can see that no value is repeated. Therefore, this data set has zero modes
