The following data set lists the midterm scores received by 50 students in a chemistry class: .Find the interquartile range. a. 24 b. 18 c. 20 d. 22 45 85 92 99 37 68 67 78 81 25 97 100 82 49 54 78 89 71 94 87 21 77 81 83 98 97 74 81 39 77 99 85 85 64 92 83 100 74 68 72 65 84 89 72 61 49 56 97 92 82
Question
The following data set lists the midterm scores received by 50 students in a chemistry class: .Find the interquartile range. a. 24 b. 18 c. 20 d. 22 45 85 92 99 37 68 67 78 81 25 97 100 82 49 54 78 89 71 94 87 21 77 81 83 98 97 74 81 39 77 99 85 85 64 92 83 100 74 68 72 65 84 89 72 61 49 56 97 92 82
Solution
To find the interquartile range, we first need to organize the data in ascending order and find the quartiles.
Here is the sorted data:
21 24 25 37 39 45 49 49 54 56 61 64 65 67 68 68 71 72 72 74 74 77 77 78 78 81 81 81 82 82 83 83 85 85 85 87 89 89 92 92 92 94 97 97 97 98 99 99 100 100
The lower quartile (Q1) is the median of the first half of the data. Since we have 50 data points, the first half is the first 25 numbers. The median of this set is the average of the 12th and 13th numbers, which are 56 and 61. So, Q1 = (56 + 61) / 2 = 58.5.
The upper quartile (Q3) is the median of the second half of the data. This is the average of the 38th and 39th numbers, which are 89 and 89. So, Q3 = (89 + 89) / 2 = 89.
The interquartile range (IQR) is Q3 - Q1 = 89 - 58.5 = 30.5.
So, none of the options (a. 24, b. 18, c. 20, d. 22) match the calculated IQR. There might be a mistake in the question or the options provided.
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