What is the interquartile range of this data set?
4,5,7,9,10,14,16,24
AAAaannndd the bot gets it wrong yet again!
The median is (9+10)/2 = 9.5
Luckily, the final answer is still correct.
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.
To find the interquartile range of a data set, you need to first find the values of the first quartile (Q1) and the third quartile (Q3). Once you have these values, you can calculate the interquartile range by subtracting Q1 from Q3.
1. Start by arranging the data set in ascending order: 4, 5, 7, 9, 10, 14, 16, 24.
2. Calculate the position of Q1 by using the formula (n + 1) / 4, where n is the total number of values in the data set. In this case, there are 8 values, so (8 + 1) / 4 = 2.25. Since the position is not a whole number, we need to find the average of the values in positions 2 and 3. The values in these positions are 5 and 7, so the average is (5 + 7) / 2 = 6.
3. Calculate the position of Q3 by using the formula 3 * (n + 1) / 4. In this case, 3 * (8 + 1) / 4 = 6.75. Again, we need to find the average of the values in positions 6 and 7. The values in these positions are 14 and 16, so the average is (14 + 16) / 2 = 15.
4. Finally, calculate the interquartile range by subtracting Q1 from Q3: 15 - 6 = 9.
Therefore, the interquartile range of the given data set is 9.
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.