Question

steven, marcos, and juan are having a free - throw shooting contest. each boy takes six turns and records the number of free throws he makes out of 10 shots. which boys median is greatest? steven: 2, 4, 6, 8, 8, 9 marcos: 3, 5, 6, 7, 8, 10 juan: 3, 5, 5, 6, 9, 9 a. steven b. marcos c. juan d. none of the above

Explanation:

Step1: Calculate Steven's median

For Steven's data \(2,4,6,8,8,9\), since \(n = 6\) (even number of data points). The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values. \(\frac{n}{2}=3\), \(\frac{n}{2}+1 = 4\). The values are \(6\) and \(8\). Median \(=\frac{6 + 8}{2}=7\).

Step2: Calculate Marcos's median

For Marcos's data \(3,5,6,7,8,10\), \(\frac{n}{2}=3\), \(\frac{n}{2}+1 = 4\). The values are \(6\) and \(7\). Median \(=\frac{6+7}{2}=6.5\).

Step3: Calculate Juan's median

For Juan's data \(3,5,5,6,9,9\), \(\frac{n}{2}=3\), \(\frac{n}{2}+1 = 4\). The values are \(5\) and \(6\). Median \(=\frac{5 + 6}{2}=5.5\).

Answer:

A. Steven