Statistics - Basic 1 - Types of Data

Types of Data

1. Numeric:

• Data that is quantifiable
• Two types of numeric data: 

1. Discrete numeric data  : Counts an event. [Example: Transaction values, No. of days, etc.] Represented by a ratio
2. Continuous numeric data: Represented by a range/interval [Example: Amount of rainfall, temperature range, etc.]

2. Categorical

• Data that has no inherent numeric meaning

1. Nominal Categorical data: Example : Gender [Man/Woman], State of birth, etc. Numbers are assigned to these values but the numbers themselves don’t mean anything. 

3. Ordinal

• Combination of numerical and categorical data. Example: Customer ratings between very satisfied[5] to not satisfied[0] for a restaurant, etc.

Mean, Median, Mode

Mean:
Given a set of data points:
x = [28, 49, 3, 78, 32, 9, 77]

Mean = Total of the values of the samples/ Number of samples. 
Mean = (28+49+3+78+32+9+77)/7 = 39.43


Median:
Sort the values and take the middle value. 
x_sorted = [3, 9, 28, 32, 49, 77, 78]
Median = 32
Here total no. of samples = 7 (odd)

For even no of samples = even
Median = average of middle values of the sorted sample

If        y_sorted = [3, 10, 33, 56, 77, 78]
Median of y_sorted= 33+56/2 = 44.5

Advantage of Median over Mean:

1. Median is less susceptible to outliers than mean.
2. If there is a high chance of outliers being present in the data set, it is wiser to take the median instead of the mean. 

Mode:
1. Mode represents the most common value in a data set. 
2. Mode is most useful when you need to understand clustering or number of ‘hits’. 

For example, a retailer may want to understand the types of refrigerator purchased so that he can set stocking labels optimally. Say, store A has a mode of ‘front_load’ while store B has a mode of ‘top_load’.

Variance, Standard Deviation

Variance:
Average of the squared differences from the mean.


Standard Deviation:
Square root of variance