Which number in the following data set is an outlier?
21 23 19 25 83 23 21
PLZ help me
83
Yes, 83.
https://www.mathsisfun.com/definitions/outlier.html
83
Yes, very good.
Thanks for the help but we need to add the part 2.
O-O
Oh, I see we have a "black sheep" in the data set. It looks like the number 83 is the outlier. It's quite the rebellious little number, standing out from the rest of the pack.
To determine if there is an outlier in a data set, you can follow these steps:
Step 1: Sort the data set in ascending order:
19, 21, 21, 23, 23, 25, 83
Step 2: Calculate the IQR (Interquartile Range):
The IQR is a measure of statistical dispersion, which helps identify outliers.
IQR = Q3 - Q1
Step 3: Calculate Q1 (first quartile) and Q3 (third quartile):
To calculate Q1 and Q3, you need to find the median (middle point) of the dataset. In this case, the sorted dataset has an odd number of values, so the median would be the middle observation, which is the 4th number, 23.
Q1: The median of the lower half of the data set, which is the median of the numbers below 23.
Q3: The median of the upper half of the data set, which is the median of the numbers above 23.
Lower half: 19, 21, 21
Upper half: 23, 25, 83
Median of the lower half (Q1): 21
Median of the upper half (Q3): 25
IQR = Q3 - Q1
IQR = 25 - 21
IQR = 4
Step 4: Identify outliers:
According to the criteria, any value that is less than Q1 - 1.5*IQR or greater than Q3 + 1.5*IQR is considered an outlier.
Lower outlier fence = Q1 - 1.5*IQR
Lower outlier fence = 21 - 1.5 * 4
Lower outlier fence = 15
Upper outlier fence = Q3 + 1.5*IQR
Upper outlier fence = 25 + 1.5 * 4
Upper outlier fence = 31
The number 83 is greater than the upper outlier fence of 31, so it is considered an outlier in this data set.
Therefore, the outlier in the given data set is 83.