Question

Methadone is a synthetic drug that has been used to help people control addiction to opiates. However, according to the voter base of a governor running for re-election, Methadone use has gotten out of hand in the state. As part of their claim, the voters sent to the governor's office the following frequency distribution summarizing the daily Methadone dosages (in milligrams) of 32 patients at a state funded clinic. Daily Methadone dosage (in milligrams) 0 to 49 50 to 99 100 to 149 150 to 199 200 to 249 Frequency 6 9 10 6 1 Based on the frequency distribution, using the midpoint of each data class, estimate the mean daily Methadone dosage for the patients. For your intermediate computations, use four or more decimal places, and round your answer to one decimal place. milligrams X​

Answer 1

To calculate the mean daily Methadone dosage for the patients, we need to first find the midpoint of each data class, which is the average of the lower and upper bounds of the class. The data classes are:

0 to 49: Midpoint = (0 + 49) / 2 = 24.5

50 to 99: Midpoint = (50 + 99) / 2 = 74.5

100 to 149: Midpoint = (100 + 149) / 2 = 124.5

150 to 199: Midpoint = (150 + 199) / 2 = 174.5

200 to 249: Midpoint = (200 + 249) / 2 = 224.5

Next, we need to multiply the midpoint of each class by the corresponding frequency and sum these values up. This will give us the numerator of the mean formula. The formula is:

Mean = (Sum of (midpoint * frequency)) / Total frequency

So, the mean can be calculated as:

Mean = (24.5 * 6 + 74.5 * 9 + 124.5 * 10 + 174.5 * 6 + 224.5 * 1) / 32

Mean = (147 + 671 + 1245 + 1044 + 224.5) / 32

Mean = 3440.5 / 32

Mean = 107.53125

Rounding to one decimal place, the mean daily Methadone dosage for the patients is 107.5 milligrams.