Given the data 21, 13, 13, 37, 13, 23, 25, 15:
A. What is the outlier in the data?
Not looking for answers, just need a demonstration on how to find the outliers, I can't figure it out.
Make a graph and look at which one seems kind of nutty. Like 37 is sort of bigger than the others
I did, and I somehow still got lost. I wish I could figure this out. I'm assuming 37 and 21 since those are really my only options, but I want to be able to prove it.
Surely not 21, since 25 is between 21 and 37.
Find the mean, and note that 37 is way farther from the mean than the other numbers.
To find the outlier in a given data set, you can follow these steps:
Step 1: Sort the data in ascending order. In this case, the sorted data would be: 13, 13, 13, 15, 21, 23, 25, 37.
Step 2: Calculate the interquartile range (IQR) by finding the difference between the first quartile (Q1) and the third quartile (Q3). To find Q1 and Q3, you need to determine the median (Q2) of the lower and upper halves of the data respectively.
Step 2a: Find Q2 (the median):
- In this case, we have 8 data points. Since it is an even number, the median is the average of the two middle values.
- Q2 = (15 + 21) / 2 = 18.
Step 2b: Find Q1 (the median of the lower half):
- Exclude the upper half of the data (18, 21, 23, 25, 37).
- The lower half of the data is: 13, 13, 13, 15.
- Since there are 4 data points, the median is the middle value.
- Q1 = 13.
Step 2c: Find Q3 (the median of the upper half):
- Exclude the lower half of the data (13, 13, 13, 15).
- The upper half of the data is: 18, 21, 23, 25.
- Since there are 4 data points, the median is the middle value.
- Q3 = 21.
Step 2d: Calculate the IQR:
- IQR = Q3 - Q1 = 21 - 13 = 8.
Step 3: Determine the acceptable range for potential outliers.
- The acceptable range for potential outliers is typically 1.5 times the IQR.
- Acceptable range = 1.5 * IQR = 1.5 * 8 = 12.
Step 4: Identify outliers.
- Any data point that is smaller than Q1 - the acceptable range or larger than Q3 + the acceptable range can be considered an outlier.
- In this case, the smallest value is 13, and Q1 - the acceptable range is 13 - 12 = 1. The largest value is 37, and Q3 + the acceptable range is 21 + 12 = 33.
- Therefore, the outlier in the data set is 37 since it is larger than the upper limit (Q3 + the acceptable range).
By following these steps, you can identify outliers in a given data set.