Which data set has the highest median?
{1, 10, 8, 29, 14, 17, 3}
{11, 15, 16, 8, 12, 14}
{8, 20, 13, 14, 12, 9}
{1, 6, 15, 7, 15, 18, 14}
the highest median is 14
may you explain you answer bot please
Certainly! To find the median of a data set, we arrange the numbers in order from smallest to largest, and then find the middle value.
For the first data set {1, 10, 8, 29, 14, 17, 3}, when we arrange the numbers in order we get:
1, 3, 8, 10, 14, 17, 29
The middle value is 10, so the median is 10.
For the second data set {11, 15, 16, 8, 12, 14}, when we arrange the numbers in order we get:
8, 11, 12, 14, 15, 16
The middle values are 14 and 15 (because there are an even number of values), so to find the median we take the average of these two values.
(14 + 15) / 2 = 14.5
So the median of this set is 14.5.
For the third data set {8, 20, 13, 14, 12, 9}, when we arrange the numbers in order we get:
8, 9, 12, 13, 14, 20
The middle value is 13, so the median is 13.
For the fourth data set {1, 6, 15, 7, 15, 18, 14}, when we arrange the numbers in order we get:
1, 6, 7, 14, 15, 15, 18
The middle value is 14, so the median is 14.
Therefore, we see that the second data set {11, 15, 16, 8, 12, 14} has the highest median, which is 14.5.
To find the data set with the highest median, we need to calculate the median for each data set and compare the values.
1) {1, 10, 8, 29, 14, 17, 3}
To calculate the median, we need to arrange the data in ascending order: {1, 3, 8, 10, 14, 17, 29}.
Since there are 7 numbers, the median is the middle value. In this case, the median is 10.
2) {11, 15, 16, 8, 12, 14}
Arranging the data in ascending order: {8, 11, 12, 14, 15, 16}.
Since there are 6 numbers, the median is the average of the middle two values. In this case, the median is (12 + 14) / 2 = 13.
3) {8, 20, 13, 14, 12, 9}
Arranging the data in ascending order: {8, 9, 12, 13, 14, 20}.
Again, there are 6 numbers, so the median is the average of the middle two values. In this case, the median is (12 + 13) / 2 = 12.5.
4) {1, 6, 15, 7, 15, 18, 14}
Arranging the data in ascending order: {1, 6, 7, 14, 15, 15, 18}.
With 7 numbers, the median is the middle value, which is 14.
Comparing the medians of each data set, we find that the data set {1, 10, 8, 29, 14, 17, 3} has the highest median, which is 10.