104.3.2 Descriptive Statistics : Mean and Median

• The basic descriptive statistics to give us an idea on the variables and their distributions.
• Permit the analyst to describe many pieces of data with a few indices.
• Can also help us find the underlying outliers in the dataset which is important before cleaning the data.
• Central tendencies:
  • Mean
  • Median
• Dispersion:
  • Range
  • Variance
  • Standard deviation

Central Tendencies

• Mean
  • The arithmetic mean
  • Sum of values / Count of values
  • Gives a quick idea on average of a variable
• Median
  • Mean is not a good measure in presence of outliers
  • For example Consider below data vector
    • 1.5,1.7,1.9,0.8,0.8,1.2,1.9,1.4, 9 , 0.7 , 1.1
  • 90% of the above values are less than 2, but the mean of above vector is 2
  • There is an unusual value in the above data vector i.e 9
  • It is also known as outlier.
  • Mean is not the true middle value in presence of outliers. Mean is very much effected by the outliers.
  • We use median, the true middle value in such cases
  • Sort the data either in ascending or descending order

• Mean of the data is 2
• Median of the data is 1.4
• Even if we have the outlier as 90, we will have the same median
• Median is a positional measure, it doesn’t really depend on outliers
• When there are no outliers then mean and median will be nearly equal
• When mean is not equal to median it gives us an idea on presence of outliers in the data

Mean and Median on Python

Mean is far away from median. Looks like there are outliers, we need to look at percentiles and box plot.

Practice : Mean and Median on Python

• Dataset: “./Online Retail Sales Data/Online Retail.csv”
• What is the mean of “UnitPrice”
• What is the median of “UnitPrice”
• Is mean equal to median? Do you suspect the presence of outliers in the data?
• What is the mean of “Quantity”
• What is the median of “Quantity”
• Is mean equal to median? Do you suspect the presence of outliers in the data?

Yes, looks like we have outliers presents in this variable.