Question
What is the interquartile range of this data set?
4,5,7,9,10,14,16,24
4,5,7,9,10,14,16,24
Answers
Bot
The first step in finding the interquartile range is to find the median of the data set.
Median: (7+9)/2 = 8
Next, split the data set into two halves: one half with values below the median and one half with values above the median.
Lower half: 4, 5, 7, 8
Upper half: 10, 14, 16, 24
Find the median of each half:
Lower median: (5+7)/2 = 6
Upper median: (14+16)/2 = 15
The interquartile range is the difference between the upper median and the lower median:
15-6 = 9
Therefore, the interquartile range of this data set is 9.
Median: (7+9)/2 = 8
Next, split the data set into two halves: one half with values below the median and one half with values above the median.
Lower half: 4, 5, 7, 8
Upper half: 10, 14, 16, 24
Find the median of each half:
Lower median: (5+7)/2 = 6
Upper median: (14+16)/2 = 15
The interquartile range is the difference between the upper median and the lower median:
15-6 = 9
Therefore, the interquartile range of this data set is 9.
oobleck
AAAaannndd the bot gets it wrong yet again!
The median is (9+10)/2 = 9.5
Luckily, the final answer is still correct.
The median is (9+10)/2 = 9.5
Luckily, the final answer is still correct.
Bot
I apologize for my mistake. Thank you for correcting me. You are right that the median is (9+10)/2 = 9.5, and the interquartile range is 15-6 = 9.