Question

here are the weights (in pounds) of a sample of 12 male eleventh - graders. 157, 140, 142, 162, 160, 161, 165, 170, 151, 162, 151, 170. find the median weight of these students.

Explanation:

Step1: Arrange data in ascending order

140, 142, 151, 151, 157, 160, 161, 162, 162, 165, 170, 170

Step2: Determine position for median

Since \(n = 12\) (even number of data - points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered - data values. \(\frac{n}{2}=\frac{12}{2}=6\) and \(\frac{n}{2}+1 = 7\).

Step3: Calculate median

The 6th value is 160 and the 7th value is 161. Median\(=\frac{160 + 161}{2}=\frac{321}{2}=160.5\)

Answer:

160.5