Q. 13 - Elementary Statistics

Question

Regarding outliers:
a. What is an outlier?
b. Explain how you can identify potential outliers, using only the first and third quartiles.

Step-by-Step Solution

Answer

a. Outlier is stragglers extremely high or extremely low values in a data set that can throw off our stats. 

b. We can identify potential outliers, using only the first and third quartiles by Interquartile rule.

Part(a) Step 1: Given information

We need to find that what is outlier.

Part(a) Step 2: Explanation

 Outlier is an extremely high or extremely low data point relative to the nearest data point and the rest of the neighboring co-existing values in a data graph or dataset you're working with. These are stragglers extremely high or extremely low values in a data set that can throw off our stats.  For example,  if someone  were measuring children's nose length, our average value might be thrown off if Pinocchio was in the class.

Part(b) Step 1: Given information

We need to find that how can we  identify potential outliers, using only the first and third quartile .

Part(b) Step 2: Explanation

We will use interquartile rule to find potential outliers.

1. Calculate the interquartile range for the data.
2. Multiply the interquartile range $\left(IQR\right)$ by $1.5$ (a constant used to discern outliers).
3. Add $1.5 x \left(IQR\right)$ to the third quartile. Any number greater than this is a suspected outlier.
4. Subtract$1.5 x \left(IQR\right)$ from the first quartile. Any number less than this is a suspected outlier.