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 (IQR). I FORGET HOW TO DO THIS
To find the interquartile range (IQR), you need to first calculate the first quartile (Q1) and the third quartile (Q3).
Here's how you can calculate the IQR step by step:
Step 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
Step 2: Find the median (Q2), which is the middle number of the data set:
Median = (73 + 76) / 2 = 74.5
Step 3: Calculate the first quartile (Q1), which is the median of the lower half of the data set:
Lower half: 59 60 61 62 63 66 69 71 72 73
Q1 = (66 + 69) / 2 = 67.5
Step 4: Calculate the third quartile (Q3), which is the median of the upper half of the data set:
Upper half: 76 77 78 80 81 81 82 83 83 84 86 88 89 91 93 94 95 96 97 98
Q3 = (89 + 91) / 2 = 90
Step 5: Calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 90 - 67.5 = 22.5
Therefore, the interquartile range (IQR) for the given data set is 22.5.
To find the interquartile range (IQR), you need to find the values corresponding to the first quartile (Q1) and third quartile (Q3).
Step 1: Arrange 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 the median:
Since there are 29 data points, the median is the 15th value, which is 82.
Step 3: Find Q1:
Q1 is the median of the lower half of the data. Counting from the beginning, the 7th value is 69.
Step 4: Find Q3:
Q3 is the median of the upper half of the data. Counting from the end, the 7th value is 89.
Step 5: Calculate the IQR:
IQR = Q3 - Q1
IQR = 89 - 69
IQR = 20
Therefore, the interquartile range (IQR) for the given data set is 20.
First you need to arrange these numbers in numerical order.
Then study this site.
http://www.childrens-mercy.org/stats/definitions/iqr.htm