Given the data 21, 13, 13, 37, 13, 23, 25, 15:
What is the outlier in the data?
What is the mean with the outlier?
What is the mean without the outlier?
A. 13; 21; 17.6
B. 37; 20; 17.6
C. 37; 17.6; 20
D. 13; 17.6; 21
To find the outlier in the data, we need to look for the value that significantly deviates from the other values.
Given the data: 21, 13, 13, 37, 13, 23, 25, 15:
1. Arrange the data in ascending order: 13, 13, 13, 15, 21, 23, 25, 37.
We can see that the value of 37 is significantly larger than the other values in the dataset. Therefore, the outlier in the data is 37.
To calculate the mean with the outlier:
1. Sum all the values in the dataset: 13 + 13 + 13 + 15 + 21 + 23 + 25 + 37 = 160.
2. Divide the sum by the total number of values in the dataset, which is 8: 160 / 8 = 20.
Therefore, the mean with the outlier is 20.
To calculate the mean without the outlier:
1. Remove the outlier, which is 37, from the dataset.
2. Sum the remaining values: 13 + 13 + 13 + 15 + 21 + 23 + 25 = 123.
3. Divide the sum by the total number of values in the dataset, which is 7 (excluding the outlier): 123 / 7 = 17.6.
Therefore, the mean without the outlier is 17.6.
So, the correct answer is C. 37; 17.6; 20.
To find the outlier in the given data, we can start by organizing the data in ascending order:
13, 13, 13, 15, 21, 23, 25, 37
An outlier is a value that is significantly different from the other values in a data set. By looking at the data, we can see that 37 is the only value that is notably larger than the others. Therefore, the outlier in the data is 37.
To find the mean with the outlier, we can add up all the values in the data set and divide by the total number of values:
Mean = (13 + 13 + 13 + 15 + 21 + 23 + 25 + 37) / 8
Mean = 160 / 8
Mean = 20
So, the mean with the outlier is 20.
To find the mean without the outlier, we need to exclude the outlier (37) from our calculations. We can add up the remaining values and divide by the total number of values (7):
Mean = (13 + 13 + 13 + 15 + 21 + 23 + 25) / 7
Mean = 123 / 7
Mean ≈ 17.6 (rounded to one decimal place)
Therefore, the mean without the outlier is approximately 17.6.
The correct answer is option C. 37; 17.6; 20.
outlier = 37
mean = ∑x/n