Calculate the interquartile range of the skewed dataset 0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10.
To calculate the interquartile range (IQR) of a dataset, we first need to find the first quartile (Q1) and the third quartile (Q3).
Given dataset: 0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10
Step 1: Arrange the data in order.
0, 2, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10
Step 2: Find the median (Q2) of the dataset. Q2 = 8.
Step 3: Split the dataset into two halves at the median.
First half: 0, 2, 6, 7, 7, 7
Second half: 9, 9, 9, 10
Step 4: Find Q1 and Q3.
For the first half:
Q1 = (6+7)/2 = 6.5
For the second half:
Q3 = (9+9)/2 = 9
Step 5: Calculate the IQR.
IQR = Q3 - Q1
IQR = 9 - 6.5
IQR = 2.5
Therefore, the interquartile range of the dataset is 2.5.