Understanding Interquartile Range in a Dataset
The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) in a dataset. It measures the middle spread of the data and represents the range where the central 50% of the data points lie.
The dataset given is: 36, 44, 44, 68, 71, 75.
To find the quartiles, we first need to find the median of the dataset, which is the middle value when the numbers are arranged in order. If there is an even number of data points, as is the case here, the median is the average of the two middle numbers.
The median is the average of the third and fourth data points: (44 + 68) / 2 = 112 / 2 = 56.
Now, Q1 (the first quartile) is the median of the first half of the dataset, and Q3 (the third quartile) is the median of the second half.
For Q1, considering the first half of the dataset: 36, 44, 44. Since there's an odd number of data points, the median is the middle number, which is 44.
For Q3, considering the second half of the dataset: 68, 71, 75. Again, the median is the middle number, which is 71.
So the interquartile range (IQR) is Q3 - Q1: 71 - 44 = 27.
The interquartile range of the dataset is 27.
