Example Question - interquartile range calculation
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Calculating Interquartile Range
To calculate the interquartile range (IQR), you first need to 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 the difference between Q3 and Q1. First, we will need to determine the position of the quartiles. There are 11 numbers in the data set you provided: 10, 25, 31, 40, 45, 51, 51, 59, 67, 96, 98 To find Q1, we need the median of the first 5 numbers (since the median - 51 - is not included in either half): 10, 25, 31, 40, 45 The median of these numbers is 31 (the middle number), so Q1 is 31. To find Q3, we take the median of the last 5 numbers: 59, 67, 96, 98 The median of these numbers is the average of 67 and 96 because there are an even number of data points: (67 + 96) / 2 = 163 / 2 = 81.5 So, Q3 is 81.5. Now, find the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 81.5 - 31 = 50.5 Therefore, the interquartile range of the provided data set is 50.5.
Calculating Interquartile Range (IQR) for a Data Set
To find the interquartile range (IQR) for a given data set, you need to subtract the first quartile (Q1) from the third quartile (Q3). The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half. The given data set: 1, 5, 5, 8, 8, 9, 9 Step 1: Find the median, which is the middle value when the data set is ordered. In this case, the median is 8 (there are 3 numbers to the left and 3 numbers to the right). Step 2: Find Q1 and Q3. - For Q1, you take the lower half of the data set, which is 1, 5, 5. The median of this half is 5. - For Q3, you take the upper half of the data set, which is 8, 9, 9. The median of this half is 9. Step 3: Subtract Q1 from Q3 to get the IQR. IQR = Q3 - Q1 = 9 - 5 = 4 So, the interquartile range of the given data set is 4.
Calculating Interquartile Range (IQR) for a Data Set
The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3) in a set of data. It measures the middle 50% of the data or the spread of the middle half of the data. First, we need to find Q1 and Q3 for the given data set: \[ 1, 2, 4, 4, 4, 4, 4, 8, 8 \] Since there are 9 data points, the median (second quartile, Q2) will be the middle value, which is the fifth value when the data is ordered - in this case, 4. To find Q1, we take the lower half of the data not including the median: \[ 1, 2, 4, 4 \] The lower half has an even number of data points (4), so Q1 will be the average of the middle two numbers in this subset: \[ Q1 = \frac{(2 + 4)}{2} = \frac{6}{2} = 3 \] Next, find Q3 by taking the upper half of the data not including the median: \[ 4, 4, 8, 8 \] The upper half also has an even number of data points (4), so Q3 will be the average of the middle two numbers in this subset: \[ Q3 = \frac{(4 + 8)}{2} = \frac{12}{2} = 6 \] Now let's calculate the IQR: \[ IQR = Q3 - Q1 = 6 - 3 = 3 \] The interquartile range for the given data set is 3.
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