The highest temperatures measured at Death Valley, California, from 1995 to 2004 are given as a dataset.
127, 125, 125, 129, 123, 126, 127, 128, 128, 125
Find the range and the interquartile range of the dataset.
To find the range, we need to subtract the smallest value from the largest value:
Range = 129 - 123 = 6
To find the interquartile range (IQR), we need to first find the first quartile (Q1) and third quartile (Q3) of the dataset.
To do this, we need to put the data in order from smallest to largest:
123, 125, 125, 125, 126, 127, 127, 128, 128, 129
There are 10 data points, so the median is the average of the 5th and 6th values:
Median = (126 + 127) / 2 = 126.5
To find Q1 and Q3, we need to find the medians of the lower half and upper half of the dataset, respectively:
Lower half: 123, 125, 125, 125, 126
Upper half: 127, 127, 128, 128, 129
Q1 = median of lower half = (125 + 125) / 2 = 125
Q3 = median of upper half = (128 + 128) / 2 = 128
Now we can find the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 128 - 125 = 3
Therefore, the range of the dataset is 6 and the IQR is 3.
To find the range of a dataset, you need to subtract the lowest value from the highest value. In this case, the highest temperature is 129 and the lowest temperature is 123.
Range = Highest value - Lowest value
Range = 129 - 123
Range = 6
Therefore, the range of the dataset is 6.
To find the interquartile range (IQR) of a dataset, you need to first find the first quartile (Q1) and the third quartile (Q3). Then, subtract Q1 from Q3.
Step 1: Arrange the dataset in ascending order:
123, 125, 125, 125, 126, 127, 127, 128, 128, 129
Step 2: Find the position of Q1:
n = number of data points = 10
Q1 position = (n + 1) / 4 = (10 + 1) / 4 = 2.75
Since 2.75 is between the second and third values, we find the average of these two values:
Q1 = (125 + 125) / 2 = 125
Step 3: Find the position of Q3:
Q3 position = 3 * (n + 1) / 4 = 3 * (10 + 1) / 4 = 8.25
Since 8.25 is between the eighth and ninth values, we find the average of these two values:
Q3 = (128 + 128) / 2 = 128
Step 4: Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 128 - 125
IQR = 3
Therefore, the interquartile range (IQR) of the dataset is 3.