Transforming data

• Transforming data​


  Standardization is a method of data transformation, involving subtracting the average and dividing by the typical income difference.

  
  

  Benefits of data transformation include accuracy, simplified summarization, and comparison of different data sets.
• Calculation & interpretation of z-scores​

  • Standardization: Z-scores help us make fair comparisons between different sets of data. They make sure that all data points are measured in the same way, showing how far each point is from the average, or "mean," in terms of standard deviation.​

  
  

  • Measurement: A Z-score tells us how much a single piece of data differs from the average of its group. It shows if the data point is above or below the average and by how much.​
• Calculation & interpretation of z-scores​ 2


  Interpretation:​

  
  

  Positive Z-scores mean the data point is higher than the average.​

  
  

  Negative Z-scores mean the data point is lower than the average.​

  
  

  A Z-score of zero means the data point is exactly equal to the average.​

  
  

  Range of Z-scores: Most Z-scores fall between -2 and +2, assuming the data follows a typical bell-shaped curve. This range covers the majority of data points. Data points beyond -3 to +3 are often seen as unusual and might need extra attention because they're far from the average.​
• Calculation & interpretation of z-scores​ 3


  Steps:​

  
  

  Collect Data: Gather grades from different schools.​

  
  

  Calculate Z-scores: Figure out how far each student's grade is from their school's average grade, using the Z-score formula.​

  
  

  Compare: Now we can compare students' grades fairly, even though they're from different schools with different grading scales. A Z-score of +1.5, for example, means a student's grade is 1.5 times better than the average at their school.​
• Box plots​


  Box plots are maps for numbers in statistics, showing their distribution and any significant differences.

  
  

  They are used for data that can be any value in a range, not just grouped into categories.

  
  

  The box in the middle represents the majority of the data, the median covers the middle 50% of the data, and the line in the middle is the median.
• Box plots 2


  Box plots show outliers, which are dots outside the lines that stretch from the box to the farthest numbers.

  
  

  They are particularly useful when data is not spread out evenly, or "skewed."

  
  

  Box plots can show both types of skewness, with the median often being a better representation of the middle number compared to the average.

  
  

  They highlight the most important parts of data, even when it's all lopsided.