Answer:
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = 3.5
Step-by-step explanation:
Given that:
Consider the following ordered data. 6 9 9 10 11 11 12 13 14
From the above dataset, the highest value = 14 and the lowest value = 6
The median is the middle number = 11
For Q1, i.e the median of the lower half
we have the ordered data = 6, 9, 9, 10
here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.
i.e
median = ![\dfrac{9+9}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B9%2B9%7D%7B2%7D)
median = ![\dfrac{18}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B18%7D%7B2%7D)
median = 9
Q3, i.e median of the upper half
we have the ordered data = 11 12 13 14
The same use case is applicable here.
Median = ![\dfrac{12+13}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B12%2B13%7D%7B2%7D)
Median = ![\dfrac{25}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B25%7D%7B2%7D)
Median = 12.5
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = Q3 - Q1
The interquartile range = 12.5 - 9
The interquartile range = 3.5