Here are yesterday's high temperatures (in Fahrenheit) in 13 U.S. cities. 50 , 56 , 56 , 58 , 60 , 61 , 63 , 66 , 67 , 71 , 71 , 80 , 83 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
To find the five-number summary and the interquartile range for the given data set, follow these steps:
1. Arrange the data in ascending order:
50, 56, 56, 58, 60, 61, 63, 66, 67, 71, 71, 80, 83
2. Find the minimum value, which is the lowest number in the data set:
Minimum = 50
3. Find the maximum value, which is the highest number in the data set:
Maximum = 83
4. Find the median, which is the middle value of the data set. Since there are 13 data points, the median will be the average of the two middle values:
Median = (60 + 63) / 2 = 61.5
5. Find the lower quartile (Q1), which separates the lowest 25% of the data set from the rest. To find Q1, we need to find the median of the lower half (first 6 values) of the data set:
Q1 = (56 + 56) / 2 = 56
6. Find the upper quartile (Q3), which separates the lowest 75% of the data set from the rest. To find Q3, we need to find the median of the upper half (last 6 values) of the data set:
Q3 = (71 + 71) / 2 = 71
7. Calculate the interquartile range (IQR), which is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 71 - 56 = 15
The five-number summary for the data set is as follows:
Minimum: 50
Lower Quartile (Q1): 56
Median: 61.5
Upper Quartile (Q3): 71
Maximum: 83
The interquartile range (IQR) is 15.