In the data set below, what is the interquartile range?
46 56 75 91 99
To find the interquartile range, we first need to find the median of the data set.
Arranging the numbers in ascending order: 46 56 75 91 99
The median is the middle number, which is 75.
Next, we divide the data set into two halves based on the median:
First half: 46 56
Second half: 91 99
Then we find the median of each half:
For the first half: Median = (46 + 56) / 2 = 51
For the second half: Median = (91 + 99) / 2 = 95
The interquartile range is the difference between the upper quartile and the lower quartile. In this case, the upper quartile (Q3) is 95 and the lower quartile (Q1) is 51.
Interquartile range = Q3 - Q1
Interquartile range = 95 - 51
Interquartile range = 44
Therefore, the interquartile range of the data set is 44.