Final answer:
The mean temperature is 64.71°F. The median temperature is 68°F. The modes are 62°F and 74°F. The first quartile is 64°F and the third quartile is 83°F.
Step-by-step explanation:
To find the mean, median, mode, first quartile, and third quartile of the high temperatures, we can start by arranging the data in ascending order:
38, 42, 61, 62, 62, 63, 64, 64, 66, 68, 72, 72, 74, 74, 77, 79, 83, 85, 90, 91, 180
Mean = sum of all the temperatures/number of temperatures = (38 + 42 + 61 + 62 + 62 + 63 + 64 + 64 + 66 + 68 + 72 + 72 + 74 + 74 + 77 + 79 + 83 + 85 + 90 + 91 + 180) / 21 = 1359 / 21 = 64.71 The median is the middle value of the data set. For an odd number of values, it is the middle value itself, and for an even number of values, it is the average of the two middle values. In this case, since we have 21 values, the median is the 11th value, which is 68. The mode is the value that appears most frequently in the data set. In this case, the modes are 62 and 74, as they appear twice each.
The quartiles divide the data into four equal parts. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half of the data. To find the first quartile, we need to find the median of the data set from the first value to the median value, which is (38, 42, 61, 62, 62, 63, 64, 64, 66, 68), and the median of these values is 64. To find the third quartile, we need to find the median of the data set from the median value to the last value, which is (72, 72, 74, 74, 77, 79, 83, 85, 90, 91, 180), and the median of these values is 83.