The following scores on the midterm exam in Chemistry 102 were recorded, 93 81 59 69 82 73 61 77 95 84 88 71 86 97 63 72 89 80 60 98 91 62 78 83 76 81 94 66 83 96 find the interquartile range.
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The interquartile range is a measure of the spread or variability of a dataset. It is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3). The first quartile represents the 25th percentile of the data, and the third quartile represents the 75th percentile.
To find the interquartile range, you need to follow these steps:
1. Sort the data in ascending order: 59 60 61 62 63 66 69 71 72 73 76 77 78 80 81 81 82 83 83 84 86 88 89 91 93 94 95 96 97 98.
2. Determine the position of the first quartile (Q1): To find the position of Q1, multiply the total number of data points by 0.25. In this case, there are 30 data points, so Q1 is at the 7.5th position. Since this is not a whole number, you need to interpolate between two values. The 7th and 8th values in the sorted data are 69 and 71, respectively. Therefore, Q1 = (69 + 71) / 2 = 70.
3. Determine the position of the third quartile (Q3): To find the position of Q3, multiply the total number of data points by 0.75. Again, there are 30 data points, so Q3 is at the 22.5th position. Interpolating between the 22nd and 23rd values gives Q3 = (89 + 91) / 2 = 90.
4. Calculate the interquartile range: The interquartile range is the difference between Q3 and Q1. In this case, the interquartile range is 90 - 70 = 20.
Therefore, the interquartile range for the given data is 20.
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).
Step 1: Organize the data in ascending order:
59, 60, 61, 62, 63, 66, 69, 71, 72, 73, 76, 77, 78, 80, 81, 81, 82, 83, 83, 84, 86, 88, 89, 91, 93, 94, 95, 96, 97, 98
Step 2: Find Q1 and Q3:
To find the values of the first quartile (Q1) and the third quartile (Q3), we need to calculate the median of the lower and upper halves of the data, respectively.
In this case, we have 30 data points, so the median is the average of the 15th and 16th values (middle two values). Q1 is the median of the first half, and Q3 is the median of the second half.
Q1 = (73 + 76) / 2 = 74.5
Q3 = (89 + 91) / 2 = 90
Step 3: Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 90 - 74.5 = 15.5
Therefore, the interquartile range of the given scores is 15.5.