Question

A manufacturing company finds out the number of defective calculators in each of the last 10 batches of 100 calculators.

Batch Number	Number of Defective Caculators
1	23
2	34
3	43
4	13
5	45
6	27
7	38
8	42
9	16
10	98

Which measure of central tendency is least impacted with or without outlier?

• A. Mean
• B. Median
• C. Mode
• D. All are impacted equally.

Answer 1

The correct option is B Median

Here, '$98$' is the Outlier.
Mean of the data(with Outlier) $=\frac{Sumofalldatapoints}{Totalnumberofdatapoints}$
Mean of the data(with Outlier) $=\frac{23+34+43+13+45+27+38+42+16+98}{10}=\frac{379}{10}$
Mean of the data(with Outlier) $=37.9$

Mean of the data(without Outlier) $=\frac{23+34+43+13+45+27+38+42+16}{9}=\frac{281}{9}$
Mean of the data(without Outlier) $=31.22$

For Median, we need to arrange the data in ascending order

Batch Number	Number of Defective Calculators
1	13
2	16
3	23
4	27
5	34
6	38
7	42
8	43
9	45
10	98

The number of observations are $10$.
Median of the data(with Outlier) = Mean of $5^{th}$ and $6^{th}$ values.
Median of the data(with Outlier) $=\frac{34+38}{2}=36$

Median of the data(without Outlier) = $5^{th}$ value
Median of the data(with Outlier) $=34$

All the $10$ observation values are different. So, there will be no Mode for this data(both for with and without Outlier).

There is a change of $6.68$ in the value of Mean(with and without Outlier) for the following data.

There is a change of $2$ in the value of Median(with and without Outlier) for the following data.

The Mode for this data does not exist.

Least impacted measure of Central tendency with or without Outlier is Median for the given data.