The data below represents the average score per game of the top 40 NBA players, rounded to the nearest whole number. Find the minimum, Q1, median, Q3, maximum for the data.
Stem l leaf
1 l 55667777888888899
2 l 00000011123445566679
3 l 135
the smallest of those numbers is(2)
(3) 135 has one bigger and one smaller so it is the median
the biggest is (1)
To find the minimum, Q1, median, Q3, and maximum for the given data, we need to first understand how to interpret the given stem-and-leaf plot.
In a stem-and-leaf plot, the stem represents the tens digit of each number, and the leaf represents the ones digit. For example, the stem "1" with the leaf "5" means that the number is 15. In the given data, we have three stems: 1, 2, and 3.
To find the minimum, we need to find the smallest number in the data. From the stem-and-leaf plot, we can see that the smallest number is 10. So the minimum is 10.
To find Q1, we need to find the lower quartile, which is the median of the lower half of the data. In the given data, the lower half of the data is: 10, 11, 22, 33. The median of this lower half is the middle number, which is 22. So Q1 is 22.
To find the median, we need to find the middle value of the data. Since we have 40 data points, the middle value would be the average of the 20th and 21st data points. From the stem-and-leaf plot, we can see that the 20th and 21st data points are 22 and 33, respectively. So the median is the average of 22 and 33, which is (22 + 33) / 2 = 27.5. However, since the data points are rounded to the nearest whole number, the median will be rounded to the nearest whole number as well. Therefore, the median is 28.
To find Q3, we need to find the upper quartile, which is the median of the upper half of the data. In the given data, the upper half of the data is: 55, 66, 77, 78, 88, 88, 88, 89, 90, 90, 90, 91, 99. The median of this upper half is the middle number, which is 88. So Q3 is 88.
To find the maximum, we need to find the largest number in the data. From the stem-and-leaf plot, we can see that the largest number is 35. So the maximum is 35.
Therefore, the minimum is 10, Q1 is 22, median is 28, Q3 is 88, and the maximum is 35.