A group of patients is recruited for a clinical trial. Their heights, recorded in centimeters, are listed in the table above. Two more patients are recruited to the study. After these patients join, the mean height is 169 cm. Which of the following could be the heights of the two new patients?
A. 146 cm and 177 cm
B. 150 cm and 188 cm
C. 165 cm and 177 cm
D. 157 cm and 186 cm
Answer:D
A group of patients is recruited for a clinical trial. Their heights, recorded in centimeters, are listed in the table above. Two more patients are recruited to the study. After these patients join, the mean height is 169 cm. Which of the following could be the heights of the two new patients?
A. 146 cm and 177 cm B. 150 cm and 188 cm C. 165 cm and 177 cm D. 157 cm and 186 cm
Explanation: D If two patients are added to the trial, there will be 12 total patients. If the mean height of 12 patients is 169 cm, then the 12 patients have a total height of 12 × 169 = 2,028 cm. The total height of the first 10 patients is 184 + 176 + 181 + 157 + 168 + 154 + 148 + 165 + 190 + 162 = 1,685 cm, so the two new patients must have a total height of 2,028 - 1,685 = 343 cm. Add up the heights and eliminate any choice that does not equal 343. Only (D) works.