Example Question - q3
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Calculating Interquartile Range of a Dataset
To find the interquartile range (IQR) of a dataset, you need to find the difference between the third quartile (Q3) and the first quartile (Q1). First, let's arrange the given data in ascending order if it is not already sorted: 1, 2, 4, 4, 4, 4, 4, 8, 8. The dataset is already sorted. The next step is to find Q1 and Q3: - The first quartile (Q1) is the median of the first half of the data. Since there are 9 data points, the first half will consist of the first 4 data points. Q1 is the median of 1, 2, 4, 4, which is the average of the 2nd and 3rd points, (2+4)/2 = 3. - The third quartile (Q3) is the median of the second half of the data. The second half of the dataset after excluding the median (4, in this case) is 4, 4, 8, 8. The median of these four numbers is the average of the 2nd and 3rd points, (4+4)/2 = 4. Now, we find the IQR: IQR = Q3 - Q1 = 4 - 3 = 1. So, the interquartile range of the given dataset is 1.
Calculating Interquartile Range from Data Set
To find the interquartile range of the data set, you must first find the first quartile (Q1), which is the median of the lower half of the data, and the third quartile (Q3), which is the median of the upper half of the data. The interquartile range is then calculated by subtracting Q1 from Q3. The data set provided is: 36, 44, 44, 68, 71, 75 Step 1: Find the median to separate the lower and upper halves of the data. Since there's an even number of data points, the median is the average of the middle two values. The middle values are the third and fourth values: Median = (44 + 68) / 2 = 112 / 2 = 56 Step 2: Find Q1, the median of the lower half of the data (not including the median of the dataset if the number of observations is odd). The lower half of the data is 36, 44, and 44. The median of these values is directly the second number (since there are an odd number of data points in the lower half): Q1 = 44 Step 3: Find Q3, the median of the upper half of the data (not including the median of the dataset if the number of observations is odd). The upper half of the data is 68, 71, and 75. The median of these values is directly the second number: Q3 = 71 Step 4: Calculate the interquartile range (IQR), which is Q3 - Q1. IQR = Q3 - Q1 IQR = 71 - 44 IQR = 27 The interquartile range for the provided data set is 27.
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