To answer these questions, we'll calculate the lower quartile (Q1), median (Q2), upper quartile (Q3), the interquartile range (IQR), and the maximum number of wins. Let's take it step by step.
1. The list, which has already been sorted in ascending order, is:
7, 9, 9, 10, 10, 13, 17, 18, 18, 19, 20, 21, 24
2. The median (Q2) is the middle value of the dataset when it's ordered from smallest to largest. As there are 13 data points, the median will be the 7th value:
7, 9, 9, 10, 10, 13, (17), 18, 18, 19, 20, 21, 24
So, median (Q2) = 17
3. The lower quartile (Q1) is the median of the data points that are to the left of the overall median. So we'll take the lower half, not including the median (since we have an odd number of data points):
7, 9, 9, 10, 10, 13
In this case, since there are 6 data points, we will find Q1 by averaging the 3rd and 4th data points:
(9 + 10) / 2 = 19 / 2 = 9.5
So, lower quartile (Q1) = 9.5
4. The upper quartile (Q3) is the median of the data points that are to the right of the overall median. So we'll take the upper half, again not including the median:
18, 18, 19, 20, 21, 24
Following the same logic as for Q1, since there are 6 data points, we'll find Q3 by averaging the 3rd and 4th data points:
(19 + 20) / 2 = 39 / 2 = 19.5
So, upper quartile (Q3) = 19.5
5. The interquartile range (IQR) is the difference between the upper and lower quartiles:
IQR = Q3 - Q1 = 19.5 - 9.5 = 10
6. The maximum number of wins is simply the last and highest value in the data set:
7, 9, 9, 10, 10, 13, 17, 18, 18, 19, 20, 21, 24
So, maximum number of wins = 24
In conclusion:
- The lower quartile (Q1) is 9.5.
- The median number of wins (Q2) is 17.
- The upper quartile (Q3) is 19.5.
- The interquartile range (IQR) is 10.
- The maximum number of wins is 24.
