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
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
1 answer