Which measure of central tendency should be used when there is an outlier
The median is usually the measure of central tendency that should be used when there is an ordinal or askewed data
Answer with explanation:
There are three measure of central tendency which is used to evaluate data
1. Mean
2. Median
3. Mode
→Mean is equal to sum of all the observation divided by total number of variate in data set.
→Median is Middle most variate in the data set when arranged in ascending or descending order.
→Mode is that variate which occurs maximum number of times in the data set.
⇒When there is outlier , you can use mean or median ,because it considers all the variate in data set.
Consider the data set
A=2,3,4,5,6,
⇒Mean of A
\(=\frac{2+3+4+5+6}{5}\\\\=4\)
⇒Median =Middle most value of data set
As Total number of observation is odd
So, Median=4
⇒Suppose , a variate , 10 is added to data set.
So, Mean of A
\(=\frac{2+3+4+5+6+10}{6}\\\\=5\)
Median =Middle most value of data set
As Total number of observation is even.
So, Median
\(\rightarrow\frac{4+5}{2}\\\\=4.5\)
→ Median is less affected by an outlier than mean.
So,→ Median is better measure of central tendency when there is an outlier.