Question
Can you help me find Q1, median, Q3 interquartile range
21,22,22,25,25,36,46,61,82
21,22,22,25,25,36,46,61,82
Answers
Answer
The possible answers are
21 22 36 60 66 82 87
21 22 36 60 66 82 87
Answered by
GPT 3.5
To find the quartiles, we first need to arrange the data in ascending order:
21, 22, 22, 25, 25, 36, 46, 61, 82
Q1 (25th percentile): There are 9 numbers in the data set, so Q1 is the 25th percentile, or (25/100)*9 = 2.25. Since this falls between the second and third numbers, we take the average of the 2nd and 3rd numbers:
Q1 = (22 + 22) / 2 = 22
Median (50th percentile): The median is the middle number in a sorted list. Since there are an odd number of data points (9 in this case), the median is the middle number:
Median = 25
Q3 (75th percentile): Q3 is the 75th percentile, or (75/100)*9 = 6.75. Since this falls between the 6th and 7th numbers, we take the average of the 6th and 7th numbers:
Q3 = (36 + 46) / 2 = 41
Interquartile Range (IQR): The interquartile range is calculated by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 41 - 22 = 19
Therefore, Q1 = 22, median = 25, Q3 = 41, and the interquartile range is 19.
21, 22, 22, 25, 25, 36, 46, 61, 82
Q1 (25th percentile): There are 9 numbers in the data set, so Q1 is the 25th percentile, or (25/100)*9 = 2.25. Since this falls between the second and third numbers, we take the average of the 2nd and 3rd numbers:
Q1 = (22 + 22) / 2 = 22
Median (50th percentile): The median is the middle number in a sorted list. Since there are an odd number of data points (9 in this case), the median is the middle number:
Median = 25
Q3 (75th percentile): Q3 is the 75th percentile, or (75/100)*9 = 6.75. Since this falls between the 6th and 7th numbers, we take the average of the 6th and 7th numbers:
Q3 = (36 + 46) / 2 = 41
Interquartile Range (IQR): The interquartile range is calculated by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 41 - 22 = 19
Therefore, Q1 = 22, median = 25, Q3 = 41, and the interquartile range is 19.
Answered by
GPT 3.5
To check the answers provided, let's calculate the quartiles and the interquartile range using the given data:
21, 22, 22, 25, 25, 36, 46, 61, 82
Q1 (25th percentile): 25% of 9 is 2.25, between the 2nd and 3rd values. Q1 = (22 + 22) / 2 = 22
Median (50th percentile): Middle value of the dataset, which is 25
Q3 (75th percentile): 75% of 9 is 6.75, between the 6th and 7th values. Q3 = (36 + 46) / 2 = 41
Interquartile Range (IQR): Q3 - Q1 = 41 - 22 = 19
Comparing the calculated values with the given options:
Q1 = 22, median = 25, Q3 = 41, IQR = 19
The closest option matches the calculated data, and the answers are as follows:
Q1 = 22
Median = 25
Q3 = 41
Interquartile Range = 19
Therefore, the given answers are correct.
21, 22, 22, 25, 25, 36, 46, 61, 82
Q1 (25th percentile): 25% of 9 is 2.25, between the 2nd and 3rd values. Q1 = (22 + 22) / 2 = 22
Median (50th percentile): Middle value of the dataset, which is 25
Q3 (75th percentile): 75% of 9 is 6.75, between the 6th and 7th values. Q3 = (36 + 46) / 2 = 41
Interquartile Range (IQR): Q3 - Q1 = 41 - 22 = 19
Comparing the calculated values with the given options:
Q1 = 22, median = 25, Q3 = 41, IQR = 19
The closest option matches the calculated data, and the answers are as follows:
Q1 = 22
Median = 25
Q3 = 41
Interquartile Range = 19
Therefore, the given answers are correct.
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