Question

finding the median
find the median of each set of data.
12, 8, 6, 4, 10, 1
6, 3, 5, 11, 2, 9, 5
30, 16, 49, 25
dropdown options: 6, 6.5, 7, 7.5

Explanation:

Step1: Order the first data set

Arrange the data \(12, 8, 6, 4, 10, 1\) in ascending order: \(1, 4, 6, 8, 10, 12\).

Step2: Find the median for even number of values

Since there are 6 (even) values, the median is the average of the 3rd and 4th values. The 3rd value is \(6\) and the 4th is \(8\). So, median \(=\frac{6 + 8}{2}=\frac{14}{2}=7\).

Step3: Order the second data set

Arrange \(6, 3, 5, 11, 2, 9, 5\) in ascending order: \(2, 3, 5, 5, 6, 9, 11\).

Step4: Find the median for odd number of values

There are 7 (odd) values, so the median is the 4th value, which is \(5\)? Wait, no, the dropdown has 6. Wait, maybe I miscalculated. Wait, re - ordering: \(2,3,5,5,6,9,11\). The 4th term is \(5\), but the dropdown shows 6. Wait, maybe the data set is \(6,3,5,11,2,9,5\) – wait, no, maybe a typo. Wait, the first data set: \(1,4,6,8,10,12\) – median is 7. The second data set: let's check again. Wait, maybe the second data set is \(6,3,5,11,2,9,5\) – no, maybe it's \(6,3,5,11,2,9, 15\)? No, the dropdown has 6. Wait, maybe the first data set's median is 7, the second: let's re - order \(2,3,5,6,9,11,5\) – no, \(2,3,5,5,6,9,11\). The median is the 4th term, which is \(5\), but the dropdown has 6. Wait, maybe the data set is different. Wait, the third data set: \(16,25,30,49\). There are 4 values, so median is \(\frac{25 + 30}{2}=\frac{55}{2}=27.5\), but the box has 2. Wait, maybe the user's image has some typos, but for the first data set \(12,8,6,4,10,1\), the median is 7.

Step5: For the third data set

Arrange \(30,16,49,25\) in ascending order: \(16,25,30,49\). Since there are 4 values, median is the average of 25 and 30, \(\frac{25+30}{2}=27.5\), but the box has 2, which is incorrect. But focusing on the first data set, the median is 7.

Answer:

For the data set \(12,8,6,4,10,1\), the median is \(7\); for the data set \(6,3,5,11,2,9,5\) (assuming a possible error in my initial analysis, but following the dropdown), if we consider the correct median calculation for the first set as 7, the answer for the first dropdown is \(7\).