Question

Which of the following is not affected by outliers in the data shown below?

Answer 1

Answer:

Median(24)

Step-by-step explanation:

Given our data as 32, 20, 21, 23, 24, 24, 101, 45, 27, 101, 10.

#we first define an outlier-Outliers are numbers in a data set that are vastly larger or smaller than the other values in the set.

We find mean of our data:

n=11

$\bar X=\frac{1}{11}(32+ 20+21+23+ 24+24+ 101+ 45+27+101+10)\\\\=\frac{1}{11}(428)=38.91$

#Hence the mean is 38.91

#Median

Is the middle most data point in a data set (arranged in ranking order):

Data: 10,20,21,23,24,24,27,32,45,101,101

Our data being odd, the median value is 24

#Mode

Mode is defined as the data point that appears most often.

From our data set 24 & 101 appears the most(appearing twice each)

*Our data is thus said to be bimodal.

#Outliers usually only affect the mean.

#However, given that our data set is bimodal, we observe that the median too is affected by the outlier values of 101

#Using the data as is, only the median(24) is not affected by the outlier data points