In the data set below, what is the interquartile range?
13 15 39 43 57
To find the interquartile range, we first need to find the lower and upper quartiles.
1. Arrange the data in ascending order: 13, 15, 39, 43, 57
2. Find the median of the data set. Since there are five numbers, the median is the middle number, which is 39.
3. Split the data set into two halves at the median to find the lower and upper quartiles.
Lower quartile (Q1) = Median of the lower half of the data (13, 15) = (13 + 15) / 2 = 14
Upper quartile (Q3) = Median of the upper half of the data (43, 57) = (43 + 57) / 2 = 50
4. Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 50 - 14
IQR = 36
Therefore, the interquartile range of the data set {13, 15, 39, 43, 57} is 36.