To find which data set has the highest median, we need to calculate the median for each data set. The median is the middle value when the numbers are arranged in order. For an even number of observations, the median is the average of the two middle numbers.
Let's find the medians for each data set:
A) { 8, 20, 13, 14, 12, 9 }
First, we sort the data: { 8, 9, 12, 13, 14, 20 }
Since there are 6 numbers (even), the median is the average of the 3rd and 4th values: (12 + 13) / 2 = 12.5
Median of A = 12.5
B) { 1, 10, 8, 29, 14, 17, 3 }
First, we sort the data: { 1, 3, 8, 10, 14, 17, 29 }
Since there are 7 numbers (odd), the median is the 4th value: 10
Median of B = 10
C) { 1, 6, 15, 7, 15, 18, 14 }
First, we sort the data: { 1, 6, 7, 14, 15, 15, 18 }
Since there are 7 numbers (odd), the median is the 4th value: 14
Median of C = 14
D) { 11, 15, 16, 8, 12, 14 }
First, we sort the data: { 8, 11, 12, 14, 15, 16 }
Since there are 6 numbers (even), the median is the average of the 3rd and 4th values: (12 + 14) / 2 = 13
Median of D = 13
Now, let's summarize the medians:
- Median of A = 12.5
- Median of B = 10
- Median of C = 14
- Median of D = 13
The highest median is in C) { 1, 6, 15, 7, 15, 18, 14 } with a median of 14.