Example Question - quartiles calculation
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Calculating Interquartile Range (IQR) of a Dataset
To find the interquartile range (IQR) of the dataset, follow these steps: 1. **Order the Data**: The data in the image is already ordered from smallest to largest. 2. **Find the Median**: The median is the middle number of the dataset. If the number of observations is odd, the median is the middle number. If the number of observations is even, the median is the average of the two middle numbers. The dataset has 13 numbers, so the median is the 7th number: 22. 3. **Split the Data into Quarters**: After finding the median, split the data into two halves. For the lower half (below the median), don't include the median if the number of data points is odd. - Lower half: 10, 14, 16, 20, 20 - Upper half: 25, 30, 36, 42, 43 4. **Find the First Quartile (Q1)**: The first quartile is the median of the lower half of the data. Since there are 5 numbers in the lower half, the median is the third number: 16. 5. **Find the Third Quartile (Q3)**: The third quartile is the median of the upper half of the data. Similarly, as there are 5 numbers in the upper half, the median is the third number: 36. The interquartile range is the difference between the third quartile and the first quartile: IQR = Q3 - Q1 IQR = 36 - 16 IQR = 20 The interquartile range of the dataset is 20.
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.
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