Calculate the interquartile range of the following data.
{35, 20, 41, 48, 79, 83, 83, 97, 120}
Q1 = 1.__
Q3 = 2.__
IQR = 3.__
Values lower than 4.__ and higher than
5.__ are considered outliers.
The outliers in this data set is 6.__
a. -40
b. -14
c. 14
d. 20
e. 38
f. 52
g. 78
h. 90
i. 120
j. 142
To find the interquartile range (IQR), we first need to find the first quartile (Q1) and the third quartile (Q3).
1. First, put the data in ascending order:
{20, 35, 41, 48, 79, 83, 83, 97, 120}
2. Identify the median (middle) of the dataset. In this case, the median is 79.
3. Split the data in half at the median:
{20, 35, 41, 48} and {83, 83, 97, 120}
4. Find the median of the lower half, which is Q1:
Q1 = (35 + 41) / 2 = 38
5. Find the median of the upper half, which is Q3:
Q3 = (83 + 97) / 2 = 90
Now that we have Q1 and Q3, we can calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 90 - 38
IQR = 52
So, the interquartile range of the data is 52.
To determine the outliers, we calculate the upper and lower boundaries:
Lower Boundary = Q1 - 1.5 * IQR
Lower Boundary = 38 - 1.5 * 52
Lower Boundary = 38 - 78
Lower Boundary = -40
Upper Boundary = Q3 + 1.5 * IQR
Upper Boundary = 90 + 1.5 * 52
Upper Boundary = 90 + 78
Upper Boundary = 168
Any values in the dataset that are lower than -40 or higher than 168 are considered outliers.
Therefore, the outliers in this data set are -40.
The correct answer is a. -40