To find the range and the interquartile range (IQR) of the dataset, follow these steps:
Finding the Range:
1. Identify the highest and lowest values in the dataset.
2. Subtract the smallest value from the largest value.
Given the dataset: 127, 125, 125, 129, 123, 126, 127, 128, 128, 125, the highest temperature is 129 and the lowest temperature is 123.
The range is calculated as:
Range = Highest Value - Lowest Value
Range = 129 - 123
Range = 6
The range of the dataset is 6.
Finding the Interquartile Range (IQR):
1. Arrange the data in ascending order.
2. Find the median (Q2), which is the middle value of the dataset. If there is an even number of observations, the median is the average of the two middle values.
3. Find the first quartile (Q1), which is the median of the lower half of the dataset (not including the median if the number of observations is odd).
4. Find the third quartile (Q3), which is the median of the upper half of the dataset (not including the median if the number of observations is odd).
5. Calculate the IQR by subtracting Q1 from Q3.
The dataset in ascending order: 123, 125, 125, 125, 126, 127, 127, 128, 128, 129
Since there are 10 data points, we find Q1 and Q3 as follows:
Q1 is the median of the first five data points: (123 + 125) / 2 = 124
Q3 is the median of the last five data points: (128 + 129) / 2 = 128.5
Now we can find the IQR:
IQR = Q3 - Q1
IQR = 128.5 - 124
IQR = 4.5
The interquartile range of the dataset is 4.5.
Therefore, the range is 6, and the interquartile range is 4.5.
