The serum cholesterol levels (in $\frac{\mathrm{mg}}{\mathrm{dL}}$ ) of 18 individuals are
\[
254,242,211,240,228,218,232,206,201,244,235,259,257,222,230,252,215,213
\]
Find $30^{\text {th }}$ and $75^{\text {th }}$ percentiles for these cholesterol levels.
(a) The $30^{\text {th }}$ percentile: $0 \frac{\mathrm{mg}}{\mathrm{dL}}$
(b) The $75^{\text {th }}$ percentile: $\square \frac{\mathrm{mg}}{\mathrm{dL}}$

Step 1 ：First, sort the data in ascending order: 201, 206, 211, 213, 215, 218, 222, 228, 230, 232, 235, 240, 242, 244, 252, 254, 257, 259

Step 2 ：Next, calculate the position (P) of the 30th and 75th percentiles using the formula: \(P = \frac{n}{100} \times N\), where n is the percentile and N is the total number of data points.

Step 3 ：For the 30th percentile, calculate P as follows: \(P = \frac{30}{100} \times 18 = 5.4\). Since this is not a whole number, take the average of the 5th and 6th values in the sorted list.

Step 4 ：For the 75th percentile, calculate P as follows: \(P = \frac{75}{100} \times 18 = 13.5\). Since this is not a whole number, take the average of the 13th and 14th values in the sorted list.

Step 5 ：So, the 30th percentile is \(\frac{215+218}{2} = 216.5\) mg/dL and the 75th percentile is \(\frac{242+244}{2} = 243\) mg/dL.

Step 6 ：Therefore, the solution is: \(\boxed{\text{(a) The 30th percentile: 216.5 mg/dL}}\) and \(\boxed{\text{(b) The 75th percentile: 243 mg/dL}}\).

Step 7 ：Check the results. The 30th percentile (216.5 mg/dL) means that 30% of the individuals have cholesterol levels below this value, and indeed, 5 out of 18 individuals have cholesterol levels below 216.5 mg/dL. The 75th percentile (243 mg/dL) means that 75% of the individuals have cholesterol levels below this value, and indeed, 13 out of 18 individuals have cholesterol levels below 243 mg/dL.